1.

The sine of the angle between the vectors a=3hati+hatj+2hatk and b=2hati-2hatj+4hatk is

Answer»

`SQRT((2)/(7))`
`(2)/(SQRT7)`
`(sqrt2)/(7)`
None of these

Solution :Given that, `a=3 hat(i)+hat(j)+2HAT(k)`
and `b=2 hat(i)-2hat(j)+4hat(k)`
Let `theta` be the angle between them.
`:. COS theta=(a.b)/(|a||b|)=((3hat(i)+hat(j)+2hat(k)))/sqrt(9+1+4)((2hat(i)-2hat(j)+4hat(k)))/sqrt(4+4+16)`
`implies cos theta=(6+(-2)+8)/(sqrt(14)sqrt(24))=12/(4sqrt(21))`
`:. SIN theta=sqrt(1-cos^(2) theta)`
`=sqrt(1-144/336)=sqrt(192/336)`
`implies sin theta =2/sqrt(7)`


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