The resultant of two vectors P and Q is R If the magnitude of Q is doubled, the new resultant vector becomes perpendicular to P Then, the magnitude of R is equal toQ = { Q ×= pq (a) cosØ

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What does p and q stand for-Transposition (p → q) ∴ (¬q → ¬p) if p then q is equiv to if not q then not p Material Implication (p → q) ∴ (¬p∨q) if p then q is equiv to not p or q Exportation ((p∧q) → r) ∴ (p → (q → r)) from (if p and q are true then r is true) we can prove (if q is true then r is true, if p is true) Importation (p → (qP Since the corresponding first and second elements are not equal, hence the two ordered pairs are not equal



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If u,v and w are noncoplanar vectors and p,q are real numbers, then the equality 3 u p v p w p v w q u 2 w q v q u = 0 holds for If u,v and w are noncoplanar vectors and p,q are real numbers, then the equality 3 u p v p w p v w q u 2 w q v q u = 0 holds for Please log in or register to add a commentAsked in Kinematics by AmarDeep01 ( 502k points) kinematicsAnswer to What is the angle between the resultants of P Q and P Q where P and Q are two vectors By signing up, you'll get thousands of
P = {r} ×Let's let q = a, so p = a1 p•q = a (a1)cos (θØ) (pq)•p = pq*p cosθ = (4/5) (a1)pq (pq)•q = pq*q cosØQ ≠ Q ×
If PQ=PQ (where P and Q are vectors) then the magnitude of vector Q is= (4/5) (a1) acosØ11 PROPOSITIONS 7 p q ¬p p∧q p∨q p⊕q p → q p ↔ q T T F T T F T T T F F F T T F F F T T F T T T F F F T F F F T T Note that ∨ represents a nonexclusive or, ie, p∨ q is true when any of p, q is true and also when both are true On the other hand ⊕ represents an exclusive or, ie, p⊕ q is true only when exactly one of p and q is true 112




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8 Find the unit vector in the direction of PQ vector where P and Q are the points (1, 2, 3) and (4, 5, 6), respectivelyThen by 21 or by 12f, neither pnor q can be zero vectors, and the angle θ cannot be 0°If vector P vector Q = vector P vector P then the angle between the vectors vector P and vector Q (a) 0°



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Question From – DC Pandey PHYSICS Class 11 Chapter 05 Question – 043 VECTORS CBSE, RBSE, UP, MP, BIHAR BOARDQUESTION TEXTThe angles between PQ and PQ wilP = { (a, r), (b, r), (r, a), (r, b), Since (a, r) ≠ (r, a) P ×If θ is the angle between pq and p, cosθ = 4/5 If Ø




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P Are these two products equal?P,q >= p (1)q (1) p (0)q (0) p (2)q (2) in P3 to find the orthogonal projection of p (x) = 3x^2 3x6 onto the line L spanned by q (x) = 2x^22x1Q = {a, b, c} ×



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If p → = 5 i ^ λ j ^3 k ^ and q → = i ^ 3 j ^5 k ^, then find the value of λ, so that p → q → and p →q → are perpendicular vectors Share with your friends Share 2Otherwise it is true The contrapositive of a conditional statement of the form If p then q is If ~ q then ~ pTo ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW Let p, q, r be three mutually perpendicular vectors of the same magnitude If a



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P q p→ q ¬p∧(p→ q) ¬p∧(p→ q) → ¬q T T T F T T F F F T F T T T F F F T T T So ¬p∧(p→ q) → ¬qis not a tautology 1 3 (0 points), page 35, problem 18 p→ q ≡¬p∨q by the implication law (the first law in Table 7) ≡q∨(¬p) by commutative lawsAnswers (1) Abhishek singh 25 Points Let P=Q=R=AMagnitude of vectorR isR= (P^2Q^22PQcosthita)where thita is angle between p and qA^2=A^2A^22A^2costhitaCosthita=1/2Thita=1*Hence angle between p and q is 1 degree 3 years agoLet p and q be statement variables which apply to the following definitions The conditional of q by p is If p then q or p implies q and is denoted by p q It is false when p is true and q is false;




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Find the angle between two vectors p and q, if p x q = pq Stack Exchange Network Stack Exchange network consists of 177 Q&A communities including Stack Overflow , the largest, most trusted online community for developersQ and Q ×If one reverses the orientation, then the formula above becomes p ↦ q −1 p q, ie, a unit q is replaced with the conjugate quaternion – the same behaviour as of axial vectors




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This is the truth table of if p then q, the first 2 digits are for p and q, the third for the conditional (001, 011, 100, 111) , this is the truth table for if not p then not q (001, 010, 101, 111) , there is a difference Using modus tollens , if p then q is equivalent to (if not q then not p) – SmootQ Feb 4 '19 at 1047P*Q is a vector perpendicular to the plane of P and Q Now any vector in the plane of P and Q can be expressed as a linear combination of P and Q Here P Q is also a linear combination of P and Q So P Q is also perpendicular to P*QIs the angle between pq and q, then the angle between p and q is θØ




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Magnitude Sum of Two vectors Vector P and Vector q is given by r^2 =p^2q^22pqcos($) _____(i) here $ indicates angle between them We are given r=pq so Squaring both the sides we get r^2=p^2q^22pq _____(ii) From (i) and (ii) we can write p^2q^22pqcos($)=p^2q^22pq therefore 2pq=2pqcos($)Subtracting a vector is the same as adding its negative The difference of the vectors p and q is the sum of p and –q p – q = p (–q) Example Subtract the vector v from the vector u Solution u – v = u (–v) Change the direction of vector v to get the vector –vP = {a, b, c} and Q = {r} P ×



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P q q p!q (p!q) p^q T T F T F F T F T F T T F T F T F F F F T T F F Since the truth values for (p!q) and p^qare exactly the same for all possible combinations of truth values of pand q, the two propositions are equivalent Solution 2 We consider howThen, it can be written as, s = p – q = p ( q) Vector addition – analytical method Parallelogram law If two vectors P and Q are represented by two adjacent sides of a parallelogram both pointing outwards, then the diagonal of the parallelogram represents the resultant of P and QSo the Engle between P and Q is 90°




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Explanation Given, → P → Q = → R So, we can write, ∣∣ ∣→ R ∣∣ ∣ = √P 2 Q2 2P Qcosθ ,where θ is the angle between the two vectors Or, R2 = P 2 Q2 2P Qcosθ Given, P 2 Q2 = R2 So, R2 = R2 2P Qcosθ Or, 2P Qcosθ = 0 So, cosθ = 0Consider the triangle formed by the vectors PQ, PQ, and 2Q It is clear that the vector P bisects 2Q, as PQP = PQP We know that by the given we have that this triangle is isosceles, and therefore the midpoint of the side represented by vector 2Q (ie the head of the vector PThe negation of the Boolean expression p ∨ (~p ∧ q) is equivalent to (1) ~p ∨ ~q asked in Mathematics by Anjali01 ( 476k points) jee main




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So, the vectors P, Q and (P Q) are coplanar vectors Now (P X Q) is the cross product of vectors P and Q We know, cross product of two vectors generate a third vector which is perpendicular to the two vectors generating it through their vector product Thus, the vector (P X Q) must be perpendicular to the vectors P and Q, that is, perpendicular to the plane containing the vectors P and Q Now, the plane containing vectors P and Q, contain vector (P QPq = pcosθ qcosØIf we have any 2 vectors P and Q, the dot product of P and Q is given by P • Q = P Q cos θ where P and Q are the magnitudes of P and Q respectively, and θ is the angle between the 2 vectors The dot product of the vectors P and Q is also known as the scalar product since it always returns a scalar value




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Suppose P and Q are two vectors If PQ = PQ than the angle between two vector is, CosX = (PQ) ×(PQ) /PQPQ CosX = 90°– Q²)/ (2 (P²Q²)) = (P²Answer is (b) Q = 0 If P Q = P Q Then Q = Q which is possible when Q = 0 (null vector)




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If the vectors 3pq;5p3q and 2pq;4p2p are pairs of mutually perpendicular vectors then sin (p^q) is here i have written p and q for p bar and q bar,those are vectors,sorry for inconvience (A)√55/4 (B)√55/8 3/16 (D)√247/16 sin (p^q) means sin of angle b/w p and q please give detailed solution please helpP – Q = P (Q) Multiplication of Vectors If k is a scalar quantity and it is multiplied by a vector A, then the scalar multiplication is given by kA If k is positive then the direction of the vector kA is the same as vector A, but if the value of k is negative, then the direction of vector kA will be opposite to the direction of vector ALet ABCD be a parallelogram such that AB= q and AD = p and angle BAD be an acute angle If r is teh vector that coincides with the altitude directed from verte




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A bird is at a point P (4 m, − 1 m, 5 m) and sees two points P 1 (− 1 m, − 1 m, 0 m) and P 2 (3 m, − 1 m, − 3 m) At time t = 0, it starts flying in a plane of the three positions, with a constant speed of 2 m / s in a direction perpendicular to the straight line P 1 P 2 till it sees P 1 &P and Q are added in a "headtotail" fashion by connecting the head of P to the tail of Q Resultant R extends from the tail of P to the head of Q forming a triangle P Q P Q P Q Method Polygon Rule The sum of three or more concurrent coplanar vectors may be accomplished by adding two vectors successively(meaning p and q cannot be parallel) If the norm symbols are removed from the left side of equation in 21 above, the result is p x q = p q sin θ (angle θ is between 0°




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Consider parallelogram with vectors p and q as sides Then vectors (pq) and (pq) are its diagonals A parallelogram with equal diagonals is a rectangleConsider the statement q For any real numbers a and b, a^2 = b^2 ⇒ a = b By giving a counterexample, prove that q is false asked in Algebra by Vikram01 ( 515k points) mathematical reasoningHow to subtract Vectors?




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– P²)) klondikegj and 110 more users found this answer helpful heart outlined Thanks 68 starAccordingtoquestion f orequilibrium sin pP = sin qQ = sin rR where, p = Anglebetween Q&R= 10 r =Anglebetween P &Q = 1500 q = Anglebetween P &R= 3600 −(10 1500) = 900 hence, PQ R= sin psin qsin r = sin 10 sin 900 sin1500 = 23 21If p and q are two unit vectors and the angle between them is 60 then (1pq)/(1pq) Get the answers you need, now!




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Let the angle between two vectors P and Q be alpha and their resultant is R So we can write R^2=P^2Q^22PQcosalpha1 When Q is doubled then let the resultant vector be R_1, So we can write R_1^2=P^24Q^24PQcosalpha2 Again by the given condition R_1 is perpendicular to P So 4Q^2=P^2R_1^23 Combining 2 and 3 we get R_1^2=P^2P^2R_1^24PQcosalpha =>2PQcosalpha=P{a, b, c} Q ×See the answer Use the inner product <




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