H [3t-2] t+3 [2t-3] (a) Find all values of t for which w and z are orthogonal. 2. Consider the vectors w= and z= (b) Compute the projection of the vector z onto w; your answer should be a vector whose components are expressions in terms of t. (c) Find a point P in R³ such that the points (0,0,0), (1,-1, 1), (4, 5, 1), and P form a rectangle. Explain your reasoning.

Q: = (4, 1, a), Q = (–2, 0, b) and v = i – 3j + 4k be two points and a vector in R³ respectively. (a)…

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Q: The plane passing through the three points A(4, –3, –4), B(-4, –3,2) and C(-3,3, –2) can be…

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Q: Point P₁ lies on the line {₁:[4,4,-3]+t[2,1,−1],tER, and point P2 lies on the line…

A: Solution : Given that the lines l1 : 4,4,-3+t2,1,-1l2 : -2,-7,2+s3,2,-3

Q: Let P and Q be the points in R3 with position vectors p = (4, -6, 1) and q = (1, -3, -5),…

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Q: Give the vector equation of the plane passing through P, Q, and R. P = (8, 8, 8), Q = (4, 0, 2), R =…

A: The answer is given below:

Q: Find the component form of v and sketch the specified vector operations geometrically, where u = 3i…

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Q: (a) Find a vector equation and symmetric equations for the line through the point (0, 14, 10) and…

A: Approach to solving the question:We are given a point (0,14,10) and a direction vector d=(2,−3,9).…

Q: The plane passing through the three points A(0, 1,3), B(3,4,3) and C(2,3, –1) can be expressed as a…

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Q: Find the equation of the plane with normal vector n = (8, 7, 3) passing through the point (4,,9) in…

A: Use equation of plane and put value