Question

If three non-zero vectors , , are such that $\vec { a }$ × = 2 $\vec { a }$ × $\overrightarrow { \mathrm { c } }$ , || = | $\overrightarrow { \mathrm { c } }$ | = 1, | $\overrightarrow { \mathrm { b } }$ | = 4 and the angle between $\overrightarrow { \mathrm { b } }$ and is cos–1$\left( \frac { 1 } { 4 } \right)$ then – 2= l $\vec { a }$ , where l is equal to :

• A. ± 2
• B. ± 4
• C. $\frac { 1 } { 2 }$
• D. $\frac { 1 } { 4 }$

Answer 1

Answer: (B)

± 4

Answer 2

× = 2 ×

̃ × ( – 2) = 0

̃ – 2 = l

Taking modulus on both sides and then squaring we get, |

– 2|2 = l2 ||2

| $\overrightarrow { \mathrm { b } }$ |2 + 4||2 – 4| $\overrightarrow { \mathrm { b } }$ | || cosq = l2||2

16 + 4 – 4 . 4 . 1. $\frac { 1 } { 4 }$ = l2.1

l2 = 16

l = ± 4