It is known that vectors p = (1 2 3), q = (-4 -4 -6), the basis frame is formed by three orthogonal unit vectors Xo, Yo, and Zo (shown in Fig. 1). Find the inner product and cross product of p and q. What is the angle between p and q? X Zo Yo

a. b. C. Consider vectors V₁=(4,-5, 6) and V₂ = (1, 2, 3). Compute the angle between vectors v₁ and v₂. Write your and then show initial equation (without values) ALL steps to compute the angle Compute the length of the projection of vector v₁ onto V₂. Write your initial equation (without values) and show all steps to compute the projection. Show all intermediate equations that you use and their solutions. For example, if you need to compute the length of a vector in your answer then show its initial equation first and then show the inserted values to solve this portion. Compute the cross product between vectors V₁ and v₂. Write your initial equation (without values) and then show all steps to compute the cross product.

If a = (2, -1, 2) and b = (3, 2, 1), answer the following. Vectors can be entered using either or the i, j, k from the Vectors %3D menu. (а) а х b 3 (b) The exact area of the parallelogram formed by a and b is (c) Sketch the vectors a, b, and a x b, along with the parallelogram formed by the vectors a and b. Submit with your handwritten work.

Compute the dot product of the vectors u and v, and find the angle between the vectors. u= (-11,0,5) and v = (1,2,3). u•v= (Type an integer or a simplified fraction.)