Let `|bar(a)|=7, |bar(b)|=11, | bar(a)+bar(b)|=10 sqrt(3)`
What is the angle between `(bar(a)+bar(b) and (bar(a)-bar(b))`?

Options

A. `(pi)/(2)`
B. `(pi)/(3)`
C. `(pi)/(6)`
D. None of these

Answer

D

Explanation

Let angle between `(vec(a)+vec(b)) and (vec(a)-vec(b)) ` be `alpha`
`cos alpha = ((vec(a)+vec(b))(vec(a)-vec(b)))/(|vec(a)+vec(b)||vec(a)-vec(b)|)`
`=((7)^(2)-(11)^(2))/(10sqrt(3)xx2sqrt(10))=((7+11)(7-11))/(20sqrt(3)xxsqrt(10))=(-18)/(5sqrt(30))`
`=(-6xx3)/(5sqrt(30))xx(sqrt(30))/(sqrt(30))=-(3sqrt(30))/(25)`
`alpha = cos ^(-1)((-3)/(5)sqrt((6)/(5)))`