The vector O A where O is origin is given by O A=2 hati+2 hatj. Now it is rotated by 45° anticlockwise about O. What will be the new vector?

Question

The vector O A where O is origin is given by O A=2 hati+2 hatj. Now it is rotated by 45° anticlockwise about O. What will be the new vector? (A) 2 √2 hatj (B) 2 hatj (C) 2 hati (D) 2 √2 hati

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/0377dbe51d1b66b38ed6d57a2273092f-.png" /> OA =2 hati+2 hatj |O A|=√4+4 ⇒ 2 √2 On rotating by an angle of 45° anticlockwise it will lie along y-axis. So vecA=2 √2 hatj

Q. The vector $O A$ where $O$ is origin is given by $O A = 2 \hat{i} + 2 \hat{j}$ . Now it is rotated by $4 5^{\circ}$ anticlockwise about $O$ . What will be the new vector?

$22 \hat{j}$

$2 \hat{j}$

$2 \hat{i}$

$22 \hat{i}$

$O A = 2 \hat{i} + 2 \hat{j}$
$∣ O A ∣ = 4 + 4$
$\Rightarrow 22$
On rotating by an angle of $4 5^{\circ}$ anticlockwise it will lie along $y$ -axis.
So $A = 22 \hat{j}$

Q. The vector OA where O is origin is given by OA=2i^+2j^​. Now it is rotated by 45∘ anticlockwise about O. What will be the new vector?

22​j^​

2j^​

2i^

22​i^