What will be the projection of vector vecA= hati+ hatj+ hatk on vector vecB= hati+ hatj ?

Question

What will be the projection of vector vecA= hati+ hatj+ hatk on vector vecB= hati+ hatj ? (A) √2( hati+ hatj+ hatk) (B) 2( hati+ hatj+ hatk) (C) √2( hati+ hatj) (D) ( hati+ hatj)

Tardigrade Admin · Accepted Answer

(A cos θ) hatB=A(( vecA ⋅ vecB/A B)) hatB=( vecA ⋅ vecB/B) hatB =(2/√2)(( hati+ hatj/√2))= hati+ hatj

Q. What will be the projection of vector $A = \hat{i} + \hat{j} + \hat{k}$ on vector $B = \hat{i} + \hat{j} ?$

$2 (\hat{i} + \hat{j} + \hat{k})$

$2 (\hat{i} + \hat{j} + \hat{k})$

$2 (\hat{i} + \hat{j})$

$(\hat{i} + \hat{j})$

$(A cos θ) \hat{B} = A (\frac{A \cdot B}{A B}) \hat{B} = \frac{A \cdot B}{B} \hat{B}$
$= \frac{2}{2} (\frac{i ^ + j ^}{2}) = \hat{i} + \hat{j}$

Q. What will be the projection of vector A=i^+j^​+k^ on vector B=i^+j^​?

2​(i^+j^​+k^)

2(i^+j^​+k^)

2​(i^+j^​)

(i^+j^​)

(Acosθ)B^=A(ABA⋅B​)B^=BA⋅B​B^ =2​2​(2​i^+j^​​)=i^+j^​

Q. What will be the projection of vector $A = \hat{i} + \hat{j} + \hat{k}$ on vector $B = \hat{i} + \hat{j} ?$

$2 (\hat{i} + \hat{j} + \hat{k})$

$2 (\hat{i} + \hat{j} + \hat{k})$

$2 (\hat{i} + \hat{j})$

$(\hat{i} + \hat{j})$

$(A cos θ) \hat{B} = A (\frac{A \cdot B}{A B}) \hat{B} = \frac{A \cdot B}{B} \hat{B}$
$= \frac{2}{2} (\frac{i ^ + j ^}{2}) = \hat{i} + \hat{j}$