Question: 1. Let a = 1- 2j + k, b= -[+ 4j - 5k, c = 51 + J-2k & d = -21 - J +

1. Let a = 1- 2j + k, b= -[+ 4j - 5k, c = 51 + J-2k & d = -21 - J + k. Answer each of the following: (i) Sketch each of the above vectors in a rectangular coordinate system for R3. (ii) Find the vector 3a - 2( b + c) - d. Determine if the vector (a + b) is orthogonal to the vector (c - d); If not, find the cosine of the angle between them. (iv) If P = (3, -1,3), Q = (1,-5,5), and R = (2,2,3), determine if the vector PQ is parallel to the vector a. (V) Find the (i) Compa ; (ii) Proja; (vi) Use cross product to find the area of the triangle PQR

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