Aspire Faculty ID #16706 · Topic: CUET 2023 · Just now
CUET 2023

LIST I LIST II
A. $|\vec A+\vec B|=|\vec A-\vec B|$ I. $45^\circ$
B. $|\vec A\times\vec B|=\vec A\cdot\vec B$ II. $30^\circ$
C. $|\vec A\cdot\vec B|=\dfrac{AB}{2}$ III. $90^\circ$
D. $|\vec A\times\vec B|=\dfrac{AB}{2}$ IV. $60^\circ$

Solution

A:
$|\vec A+\vec B|=|\vec A-\vec B| \Rightarrow \vec A\cdot\vec B=0$
$\Rightarrow$ angle $=90^\circ$ → III

B:
$|\vec A\times\vec B|=\vec A\cdot\vec B$
$AB\sin\theta=AB\cos\theta \Rightarrow \theta=45^\circ$ → I

C:
$|\vec A\cdot\vec B|=AB\cos\theta=\dfrac{AB}{2}$
$\Rightarrow \cos\theta=\dfrac12 \Rightarrow \theta=60^\circ$ → IV

D:
$|\vec A\times\vec B|=AB\sin\theta=\dfrac{AB}{2}$
$\Rightarrow \sin\theta=\dfrac12 \Rightarrow \theta=30^\circ$ → II

Correct Matching:
A-III, B-I, C-IV, D-II

Previous 10 Questions — CUET 2023

Nearest first

Next 10 Questions — CUET 2023

Ascending by ID
Ask Your Question or Put Your Review.

loading...