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.

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A: We can write the answer in the below steps.

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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

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A: we have to find the line equation passing through point (4,5,-1) and perpendicular to the vectors…

Q: b Find all vectors W (W₁, W2, W3) that satisfy the equation: (3,1,4) x W = (-3,1,2).

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A: In this question we need to multiply vectors by constant and have to find values of constant

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Q: (2) Let vị = ( 2 = (2),v3 1 of the vector space R³. (2a) Does the vector v = (6 belong to…

A: Linearly independent vectors: The set of vectors v1, v2, ..., vn is said to be linearly independent…

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A: The answer is given below:

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A: To find Whether the given vectors are limearly independent or not.