The component of vector vecA=2 hati+3 hatj along the direction of ( hati- hatj) is

Question

The component of vector vecA=2 hati+3 hatj along the direction of ( hati- hatj) is (A) (1/√2) (B) -(1/√2) (C) (1/2) (D) -(1/2)

Tardigrade Admin · Accepted Answer

Given: vecA=2 hati+3 hatj, vecB=2 hati- hatj (say) Component of vecA along the direction of vecB =( vecA⋅ vecB/B) =((2 hati+3 hatj)⋅( hati - hatj)/√2) =-(1/√2)

Q. The component of vector $A = 2 \hat{i} + 3 \hat{j}$ along the direction of $(\hat{i} - \hat{j})$ is

$\frac{1}{2}$

$- \frac{1}{2}$

$\frac{1}{2}$

$- \frac{1}{2}$

Given : $A = 2 \hat{i} + 3 \hat{j}$ ,
$B = 2 \hat{i} - \hat{j}$ (say)
Component of $A$ along the direction of $B$
$= \frac{A \cdot B}{B}$
$= \frac{( 2 i ^ + 3 j ^ ) \cdot ( i ^ - j ^ )}{2}$
$= - \frac{1}{2}$

Q. The component of vector A=2i^+3j^​ along the direction of (i^−j^​) is

2​1​

−2​1​

21​

−21​

Given : A=2i^+3j^​, B=2i^−j^​ (say) Component of A along the direction of B =BA⋅B​ =2​(2i^+3j^​)⋅(i^−j^​)​ =−2​1​

Q. The component of vector $A = 2 \hat{i} + 3 \hat{j}$ along the direction of $(\hat{i} - \hat{j})$ is

$\frac{1}{2}$

$- \frac{1}{2}$

$\frac{1}{2}$

$- \frac{1}{2}$

Given : $A = 2 \hat{i} + 3 \hat{j}$ ,
$B = 2 \hat{i} - \hat{j}$ (say)
Component of $A$ along the direction of $B$
$= \frac{A \cdot B}{B}$
$= \frac{( 2 i ^ + 3 j ^ ) \cdot ( i ^ - j ^ )}{2}$
$= - \frac{1}{2}$