Question

Let ≡, ≡ and $\overline { \mathrm { c } }$ = $\hat { \mathbf { i } } + \hat { \mathbf { j } } - 2 \hat { \mathrm { k } }$ be three vectors. A vector in the plane of and $\overline { \mathrm { c } }$ whose projection on is of magnitude $\sqrt { \frac { 2 } { 3 } }$ is

• A. , –
• B. ,
• C. –,
• D. ,

Answer 1

Answer: (A)

, –

Answer 2

Let be a vector in the plane of b and c

⇒ = () + μ ( $\hat { \mathbf { i } } + \hat { \mathbf { j } } - 2 \hat { \mathrm { k } }$ ) .

Its projection on = =$\frac { 1 } { \sqrt { 6 } }$[2 +2 μ - 2 - μ -1 - 2μ ]

= $\frac { - ( 1 + \mu ) } { \sqrt { 6 } }$

⇒ $\frac { - ( 1 + \mu ) } { \sqrt { 6 } }$= $\pm \sqrt { \frac { 2 } { 3 } }$

⇒ –(1 + μ) = ± 2 ⇒ μ = 1, –3

⇒ R ≡ and –