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The angle between the line r=(hat(i)+2...

The angle between the line
`r=(hat(i)+2hat(j)-hat(k))+lamda(hat(i)-hat(j)+hat(k))` and the plane `r*(2hat(i)-hat(j)+hat(k))=4` is

A

0

B

`(pi)/(2)`

C

`pi`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Here, `b=hat(i)-hat(j)+hat(k)andn-2hat(i)-hat(j)+hat(k)`
`:." "sintheta=((hat(i)-hat(j)+hat(k))*(2hat(i)-hat(j)+hat(k)))/(sqrt(1+1+1)sqrt(4+1+1))`
`=(4)/(3sqrt(2))=(2sqrt(2))/(3)`
`rArr" "theta=sin^(-1)(2sqrt(2)/(3))`
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