Question: Please answer these two questions ASAP, no need for explanations just showing the working out is totally fine. Instead of using dy/dx please use y'

Please answer these two questions ASAP, no need for explanations just showing the working out is totally fine. Instead of using dy/dx please use y' or y" instead thanks.

(VECTORS/CALCULUS)

1. Let a: 2i+3j and b = 3j+9k. Find (a) a unit vector in the direction of c = a + b; (3 marks) {11) a x b; (3 marks) (c) the scalar component 0! and the vector component v, of a in the direction of b. (4 marks) 2. A straight line & and a plane P are defined by (: x=5+t y=5+t z=20+4t, teR and P: Arty+ z = 63. (a) Show that & passes through the origin; (2 marks) (b) Determine the angle 0 (in degrees) between & and P. (3 marks) (c) Determine the point of intersection of & and P. (4 marks)

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