Find the angle between v and w. (5 Points) Consider the vectors v = (-1.2,2) and

Question

Find the angle between v and w.

(5 Points) Consider the vectors v = (-1.2,2) and w = (1,1,4) in R3. Find the angle between v and w. What is the angle between v and v x w? Find an equation of the plane through the point P = (1,2,3) that is orthogonal to v and w. (5 Points) Consider the plane V in R3 with equation 2x - 3y + 4z = -12 and the point P = (3,-4.7). Let L be the line through the point P that is orthogonal to the plane P. Determine the point Q, where the plane P intersects the line L. Find the distance between the point P and the plane V. (5 Points) Consider the vector-valued function : R rightarrow R3. where f(t) = (a coswt, b sin wt.ct) and a, b, R are positive constants. Determine the derivative Find a vector parametrization of the tangent line to the path described by at the point (a, 0,0) = (0).

Explanation / Answer

cos inv [(v.w)/ mod v*mod w]

= cos inv (9/3sqrt 2)= 30 deg or pi/6 rad

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