JEE Main 202122 JulyMorning Shift
- Exam
- JEE Main
- Year
- 2021
- Date
- 22 July
- Shift
- Morning Shift
- Subject
- Physics
- Chapter
- Mathematics in Physics
JEE Main 2021 · 22 July · Morning Shift · Physics · Mathematics in Physics
What will be the projection of vector → A = ^ i + ^ j + ^ k on...
What will be the projection of vector \overset{\to}{A} = \overset{^}{i} + \overset{^}{j} + \overset{^}{k} on vector \overset{\to}{B} = \overset{^}{i} + \overset{^}{j} ?
Options
- A\sqrt{2} ( \overset{^}{i} + \overset{^}{j} + \overset{^}{k} )
- B2\left(\overset{^}{i} + \overset{^}{j} + \overset{^}{k}\right)
- C\sqrt{2} ( \overset{^}{i} + \overset{^}{j} )
- D( \overset{^}{i} + \overset{^}{j} )
Correct answer
D. ( \overset{^}{i} + \overset{^}{j} )
Step-by-step solution
\left(Acos\theta\right)\overset{^}{B} = A\left(\dfrac{\overset{\to}{A} \cdot \overset{\to}{B}}{AB}\right)\overset{^}{B} = \dfrac{\overset{\to}{A} \cdot \overset{\to}{B}}{B}\overset{^}{B}
= \dfrac{2}{\sqrt{2}}\left(\dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}}\right) = \overset{^}{i} + \overset{^}{j}
= \dfrac{2}{\sqrt{2}}\left(\dfrac{\overset{^}{i} + \overset{^}{j}}{\sqrt{2}}\right) = \overset{^}{i} + \overset{^}{j}