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If 1/2,1/3,n are direction cosines of a ...

If `1/2,1/3,n` are direction cosines of a line, then the value of `n` is

A

`(sqrt(23))/6`

B

`23/6`

C

`2/3`

D

`3/2`

Text Solution

Verified by Experts

The correct Answer is:
A
If `(1/2,1/3,n)` are the DC's of line, ten using the relation
`l^(2),m^(2),n^(2)=1`
`=(1/2)^(2)+(1/3)^(2)+n^(2)=1`
`implies n^(2)-1-1/4-1/9`
`implies n^(2)=23/36impliesn=(sqrt(23))/6`
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