15. Find in rectangular components the unit vector which is: (a) in the direction of E at P(2,3,-4) if E = (x² + y² +2²)(xa/√y² + z² + ya,/√√x² + z² + za₂/√x² + y²); (b) perpendicular to the plane passing through M(1,-5,5), N(-2,4,0), and Q(2,3,4), and having a positive x component. (c) Find the angle between the vectors RMN and RMQ-

5. [7.6] If vectors ū=(5,2,-1) and = (2,-1, 3) then... a) determine u x v. b) Explain the geometric significance of the result found in part a).

the space curve (t) = (2t, t², 2t)

12. Consider the vectors v1 = (2, -1, 5), v2 = (1, 3, -4), V3 = (-3, –9, 12) in R³. (a) Show that {v1, v2, V3} is linearly dependent. (b) Is vị E span{v2, v3}? Draw a picture illustrating your answer.