1. Determine the relation between 9 and h so that is orthogonal to W. u=3;-2j tk, v=jtaj - 3k, w = -j tj tak 2. Determine scalars g and h 50 that w-gy-hy is 3. gu thv orthogonal to both us and y.. y= i tj -2k, v = -i tajt 3k, w = Sitsk Establish relationships given. Introduce the unit vectors i,j,k. (uty) (-) 4. Show that if w is orthogonal to u and to v, then wis orthogonal to ant Bu for all scalars x and B.

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: Let fery) Ts TS a diff eran tiable function. eron The directional Jeri ve dive of fuiyl in the direc…

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Q: 4 В T(t+h) A 21 y 01 2

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Q: 32. Determine the vector equation of the plane that contains the following two lines. L1: = [4,-3,…

A: .

Q: Let P(3,-1,4) and Q(10, 13,9) u = (2,5, -1) and v= (7,-1,2) l be the line through P along direction…

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Q: 8. If it [13,7.-2] is orthogonal to v v=[-5, k.7], determine the value(s) of k.

A: Given query is to find the value of k.n

Q: 11. Let / be the intersection of the two planes 2x - 3y + 4z = 2 and x-z = 1 a. Find a vector…

A: Let l be the intersection of the following two planes(a) To find a vector equation of l.(b) To find…

Q: Determine vector and parametric equations for the line in R that passes through the points A(1,0, 1,…

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Q: b) Find parametric and vector equations for the line through (2,3,0) perpendicular to the vectors u…

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Q: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

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Q: Find vectors u and v such that the parametric equation of the line y= mx + b can be expressed as…

A: Given that  equation of the line is  y= mx + b…