Solveeit Logo
Login

Question

Question: The projection of the vector \(\vec { A } = \hat { i } - 2 \hat { j } + \hat { k }\) on the vector ...

The projection of the vector A⃗=i^−2j^+k^\vec { A } = \hat { i } - 2 \hat { j } + \hat { k } on the vector B→=4i^−4j^+7k^\overrightarrow { \mathrm { B } } = 4 \hat { \mathrm { i } } - 4 \hat { \mathrm { j } } + 7 \hat { \mathrm { k } } is

A

199\frac { 19 } { 9 }

B

389\frac { 38 } { 9 }

C

89\frac { 8 } { 9 }

D

49\frac { 4 } { 9 }

Answer

199\frac { 19 } { 9 }

Explanation

Solution

Here, A⃗=i^−2j^+k^\vec { A } = \hat { i } - 2 \hat { j } + \hat { k }

B→=4i^−4j^+7k^\overrightarrow { \mathrm { B } } = 4 \hat { \mathrm { i } } - 4 \hat { \mathrm { j } } + 7 \hat { \mathrm { k } }

The projections of on B⃗\vec { B } =Acos⁡θ= A \cos \theta

=4+8+781=199= \frac { 4 + 8 + 7 } { \sqrt { 81 } } = \frac { 19 } { 9 }