The measure of acute angle between the lines whose direction ratios are `3, 2, 6 and `-2, -1, 2` is

Options

A. `cos^(-1)(1/7)`
B. `cos^(-1)(8/15)`
C. `cos^(-1)(1/3)`
D. `cos^(-1)(8/21)`

Answer

D

Explanation

Here , ` a_(1) = 3, b_(1) = 2, c_(1) = 6 and a_(2) = - 2, b_(2) = 1, c_(2) = 2`.
We have,
`cos theta = |(a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2))/(sqrt(a_(1)^(2)+b_(1)^(2)+c+_(1)^(2.))sqrt(a_(2)^(2)+b_(2)^(2)+c_(2)^(2)))|`
`:. cos theta = |(3(-2)+2(1)+6(2))/(sqrt(3^(2)+2^(2)+6^(2.))sqrt((-2)^(2)+1^(2)+2^(2)))|`
` = |(-6+2+12)/(sqrt(49)*sqrt9)|`
` = |8/(7 xx 3)| = |8/21|`
` :. " " theta = cos^(-1) (8/21)` .
Hence , the correct answer from the given alternatives is (d) .