Question

If $\vec { a } , \vec { b } , \vec { c }$ are such that [ $\vec { a } , \vec { b } , \vec { c }$ ] = 1, $\overrightarrow { \mathrm { c } } = \lambda ( \vec { a } \times \vec { b } )$ $\vec { a } ^ { \wedge } \vec { b } < \frac { 2 \pi } { 3 }$ , and $| \vec { a } |$ = $\sqrt { 2 }$, = , then the angle between and is

• A. $\frac { \pi } { 6 }$
• B. $\frac { \pi } { 4 }$
• C. $\frac { \pi } { 3 }$
• D. $\frac { \pi } { 2 }$

Answer 1

Answer: (B)

$\frac { \pi } { 4 }$

Answer 2

1 =

$\frac { 1 } { 3 } = \frac { 1 } { 9 }$ = (a2 b2 sin2q) =$\frac { 1 } { 9 }$× 2 × 3 sin2q

̃ sin²q = $\frac { 1 } { 2 }$ \ q = $\frac { \pi } { 4 }$