The ratio in which the plane `vecr.(veci-2 vecj+3veck)=17` divides the line joining the points `-2veci+4vecj+7veckandvec3i-5vecj+8veck` is

Options

A. `1:5`
B. `1:10`
C. `3:5`
D. `3:10`

Answer

d

Explanation

Let the plane `vecr.(veci-2vecj+3veck)=17` divide the line
joining the points `-2veci+4vecj+7veckand3veci-5vecj+8veck` in the ration t : 1 at point P is
Therefore, point P is
`(3t-2)/(t+1)veci+(-5t+4)/(t+1)vecj+(8t+7)/(t+1)veck`
This lies on the given plane
`because(3t-2)/(t+1).(1)+(-5t+4)/(t+1)(-2)+(8t+7)/(t+1)(3)=17`
Solving, we get
`t=(3)/(10)`