Question

If vector a=i+j+k and vector b=j-k, find a vector c such that vector(a*b)=vector b and (a.c)=3

Answer 1

Let c = xi + yj + 2k

Now

a.c = x + y + z = 3

Now

arc = (i + j + k) × (xi + yj + 2k) 

= (z − y)i + (x − z)j + (y − x)k

= j − k

Now z − y = 0 hence z = y

Now x − z = 1 and y − x = −1

x + y + z = 3

1 + z + z + z = 3

\(z = \frac 23 = y\)

\(x = \frac 53\)

\(c = \frac{5i + 2j + 2k}3\)

Answer 2

Given vector a=i+j+k and vector b=j-k