Question

A unit vector is orthogonal to 5+ 2+ 6 and is coplanar to 2+ + and – + then the vector is –

• A.
• B.
• C.
• D. $\frac { 2 \hat { i } + 2 \hat { j } - \hat { k } } { 3 }$

Answer 1

Answer: (A)

Answer 2

Let $\vec { a }$ be the unit vector

̃ $\vec { a }$ = a(2+ + ) + b(– + )

̃ | $\vec { a }$ | = 1 ̃ (2a + b)2 + (a – b)2 + (a + b)2 = 1

̃ 6a2 + 4ab + 3b2 = 1

$\vec { a }$ is orthogonal to 5+ 2+ 6 so,

̃ 5(2a + b) + 2(a – b) + 6(a + b) = 0

̃ 18a + 9b = 0 ̃ 2a = – b

\ 6a2 – 8a2 + 12a2 = 1

̃ 10a2 = 1

̃ a = ± $\frac { 1 } { \sqrt { 10 } }$ ̃ b = $\mp$ $\frac { 2 } { \sqrt { 10 } }$

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