A. Find a nonzero vector orthogonal to the plane through the points  P, Q, and R. B. Find the area of triangle PQR. P (1,0,1),  Q(-2,1,3),  R(4,2,5)

Q: 3. Determine the value of a and b if the vectors à = [a, 26, 32] and b = [49,-91,b] are collinear.

A: Given,            Two vectors are a→=a,26,32 and b→=49,-91,b are collinear.To find : Determine the…

Q: Find the angle between two vectors ū = (1, –1,0), and ở = (2, –1,2) %3D

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Q: Find the vector v = PQ. P = (4,3, 6) Q = (9,5, 3) V =

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Q: The point t has coordinater (4.1), AB = |- || B² 1-5. Find the coordinater of 5 ance the column…

A: We have to solve given problems:

Q: 6. Write DÉ as a linear combination of the vectors i and j a) D (9,-6) E (-7, 2) first write in…

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (2, 5, 3), Q = (– 3, –…

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Q: 2. Let vectors a = (3, 1, 2), b = (0, 2, 1), and c = (1, 1, -1) be given. Find (2a + 3b). c. • Find…

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Q: 1. The vertices of a triangle are located at A(4,1, –3), B(-2,5,4) and C(0, 1, 6). Using vector…

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Q: 5. Write the components of the following vectors: 5a. ˆı, 5b. −7ˆȷ, 5c. 4ˆı + 9ˆȷ, 5d. 5ˆı − 3ˆȷ.6.…

A: The objective of the question is to write the components of the given vectors and to express the…

Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

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Q: The vectors a=⟨2,3,z⟩ and b=⟨1,2,z⟩ are orthogonal to c=⟨z,r3,−z⟩, where z and r are nonzero real…

A: Given:Vector a=2,3,z,b=1,2,z are orthogonal to c=z,r3,-z

Q: 1. Perform the stated operations on the vectors u, v and w. u=3i-k, v=i-j+2k, w = 3j (a) w-v (b)…

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Q: a. Write the vector (8,5, 30) as a linear combination of a₁ = (4, -4,1), d₂ =(4,-5, 5) and d3 = (0,…

A: (a) Let,   <8, 5, 30> = a<4, -4, 1> + b <4, -5, 5>+ c<0, -4, -4>     =>…