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Question: A unit vector <img src="https://cdn.pureessence.tech/canvas_632.png?top_left_x=600&top_left_y=300&wi...

A unit vector in the plane b→=2i^+j^\overrightarrow { \mathrm { b } } = 2 \hat { \mathrm { i } } + \hat { \mathrm { j } } and is such that where is

A

i^+j^+k^3\frac { \hat { \mathrm { i } } + \hat { \mathrm { j } } + \hat { \mathrm { k } } } { \sqrt { 3 } }

B
C
D

2i^+j^5\frac { 2 \hat { \mathrm { i } } + \hat { \mathrm { j } } } { \sqrt { 5 } }

Answer
Explanation

Solution

Let a⃗=λb⃗+μc⃗\vec { a } = \lambda \vec { b } + \mu \vec { c }

then a⃗⋅b⃗ab=a→⋅d→ad\frac { \vec { a } \cdot \vec { b } } { \mathrm { ab } } = \frac { \overrightarrow { \mathrm { a } } \cdot \overrightarrow { \mathrm { d } } } { \mathrm { ad } }

i.e.

i.e.

= [λ(2i^+j^)+μ(i^−j^+k^)]⋅(j^+2k^)5\frac { [ \lambda ( 2 \hat { \mathrm { i } } + \hat { \mathrm { j } } ) + \mu ( \hat { \mathrm { i } } - \hat { \mathrm { j } } + \hat { \mathrm { k } } ) ] \cdot ( \hat { \mathrm { j } } + 2 \hat { \mathrm { k } } ) } { \sqrt { 5 } }
i.e. l (4 + 1) + m(2 – 1) = l(1) + m(–1 + 2)

i.e. 4l = 0 i.e. l = 0 \