Answer to Question #210880 in Linear Algebra for Ree

Question

Question 5:

(5.1)Assume that a vector a of length ||a|| = 3 units. In addition, a points in a direction that is 135◦ counterclockwise from the positive x-axis, and a vector b in th xy-plane has a length ||b|| = 1 3 and points in the positive y-direction.

(5.2) Find a ·b. Calculate the distance between the point (−1,√3) and the line 2x-2y-5=0

Question 6

Let u =< −2,1,−1,v =< −3,2,−1 >and w =< 1,3,5 >. Compute:

(6.1) u ×w,

(6.2)u ×(w ×v)and(u × w)×v.

Question 7

(7.1) (Find a point-normal form of the equation of the plane passing through P = (1,2,−3) and having n =< 2,−1,2 > as a normal.

(7.2) Determine in each case whether the given planes are parallel or perpendicular: (a) x +y +3z +10=0andx +2y −z =1,

(b)3x −2y +z −6=0and4x +2y −4z =0, (c)3x +y +z −1=0and−x +2y +z+3=0,

(d)x −3y +z+1=0and3x −4y +z−1=0.

Answer 1

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