Question

Let the unit vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ be perpendicular and the unit

vector $\overrightarrow{C}$ be inclined at an angle q to both $\overrightarrow{A}$and $\overrightarrow{B}$. If C = a$\overrightarrow{A}$+b$\overrightarrow{B}$+g($\overrightarrow{A}$ × $\overrightarrow{B}$) then

• A. a = b
• B. g²= 1– 2a²
• C. g² = – cos 2q
• D. b²=$\frac{1 + \cos 2\theta}{2}$

Answer 1

Answer: (B)

g²= 1– 2a²

Answer 2

= $\alpha \overrightarrow { \mathrm { A } } \cdot \overrightarrow { \mathrm { A } } + \beta \overrightarrow { \mathrm { B } } \cdot \overrightarrow { \mathrm { A } } + \gamma \overrightarrow { \mathrm { A } } \cdot ( \overrightarrow { \mathrm { A } } \times \overrightarrow { \mathrm { B } } ) = \alpha$ or a = cos q also =

Ž b = cos q again = $2 \overrightarrow { \mathrm { C } } \cdot \overrightarrow { \mathrm { A } } + \beta \overrightarrow { \mathrm { B } } \cdot \overrightarrow { \mathrm { C } } + \gamma \overrightarrow { \mathrm { C } } \cdot ( \overrightarrow { \mathrm { A } } \times \overrightarrow { \mathrm { B } } )$

= a cosq + b cos q + g²

or 1 = 2a cos q + g² Ž 1 = 2a² + g²