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The angles with a vector hat(i)+hat(j)+s...

The angles with a vector `hat(i)+hat(j)+sqrt(2hat(k))` makes with X,Y and Z axes respectively are

A

`60^@`,`60^@`,`60^@`

B

`45^@`,`45^@`,`45^@`

C

`60^@`,`60^@`,`45^@`

D

`45^@`,`45^@`,`60^@`

Text Solution

Verified by Experts

The correct Answer is:
C
`vecR=hati+hatj+sqrt(2)hatk`
Comparing the given vector with `R=R_(x)hati+R_(y)hatj+R_2hatk`
`R_x=1,R_(y)=1,R_(z)=sqrt(2)` and `|vecR|=sqrt(R_x^(2)+R_(y)^(2)+R_(z)^(2))=2`
`cosalpha=(R_x)/(R)=(1)/(2)impliesalpha=60^(@)`
`cosbeta=(R_y)/(R)=(1)/(2)impliesbeta=60^@`
`cosgamma=(R_2)/(R)=(1)/(sqrt2)impliesgamma=45^@`
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