Solve the problem Find a so that the vectors v i aj and w

Solve the problem. Find a so that the vectors v = i + aj and w = -2i - 4j are orthogonal. 2 1/2 -2 -1/2 -1 Find the position vector for the vector having initial point P and terminal point Q. P = (-1, 3, -1) and Q = (1, 0, -2) v = 3i - 2j + 2k v = -2i - 3j + 2k v = -2i + 3j + 2k v = 2i - 3j + 4k v = 2i - 3j - 2k

Solution

v=i + aj      w=-2-4i

In case of orthogonal,theta=pi/2

v.w=IvIIwI cos pi/2

cos pi/2=0

v.w=0

v.w= 1(-2) +a(-4)

v.w= -2 -4a

-2-4a=0

a=-1/2

Correct option is D

7. P=(-1,3,-1) Q= (1,0,-3)

position vector= terminal vector-initial vector

                    = (1-(-1))i + (0-3)j+ (-3-(-1))k = 2i -3j -2k

Correct option is E