Question

If = (1, 1, 1), = (1, 1, –1) and $\overrightarrow { \mathrm { a } }$ and $\overrightarrow { \mathrm { b } }$ are two vectors such that = 2 + $\overrightarrow { \mathrm { b } }$ and $\overrightarrow { \mathrm { e } _ { 2 } }$ = + 2 $\overrightarrow { \mathrm { b } }$ , then the angle between & is

• A. cos–1 $\left( \frac { 7 } { 9 } \right)$
• B. cos–1 $\left( \frac { 7 } { 11 } \right)$
• C. cos–1 $\left( - \frac { 7 } { 11 } \right)$
• D. sin–1$\left( \frac { 6 \sqrt { 2 } } { 11 } \right)$

Answer 1

Answer: (C)

cos–1 $\left( - \frac { 7 } { 11 } \right)$

Answer 2

̃ 3 = (1, 1, 3) and 3 = (1, 1, – 3)

= $\left( \frac { 1 } { 3 } , \frac { 1 } { 3 } , 1 \right)$ and = $\left( \frac { 1 } { 3 } , \frac { 1 } { 3 } , - 1 \right)$

cos q = = $\frac { \frac { 1 } { 9 } + \frac { 1 } { 9 } - 1 } { \sqrt { \frac { 11 } { 9 } } \sqrt { \frac { 11 } { 9 } } }$ = –$\frac { 7 } { 11 }$

̃ q = cos–1 $\left( - \frac { 7 } { 11 } \right)$