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The ratio in which the plane vec rdot...

The ratio in which the plane ` vec rdot` `(vec i-2 vec j+3 vec k )`=17 divides the line joining the points ` -2 vec i+4 vec j+7 vec k and 3 vec i-5 vec j+8 vec k` is a. `1:5` b. `1: 10` c. `3:5` d. `3: 10`

A

`1:5`

B

`1:10`

C

`3:5`

D

`3:10`

Text Solution

Verified by Experts

The correct Answer is:
d
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)`
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