Question

Given two vectors A = 5i + 6j + 8k and

B= 3i + 4j. What is the scalar projection of A
on B?

Answer 1

EXPLANATION

>>Given Vectors :

$\circ \: \: \: \: \sf \vec{A} = 5 \hat{i} + 6 \hat{j} + 8 \hat{k}$

$\circ \: \: \: \: \sf\vec{B} = 3 \hat{i} + 4 \hat{j}$

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~Formula

$\sf : \to \vec{A}. \vec{B} = |A| |B| \sin \phi$

>>Scalar Product :

$\mapsto\sf \vec{A} .\sf\vec{B} = (5 \hat{i} + 6 \hat{j} + 8 \hat{k})( 3 \hat{i} + 4 \hat{j})$

$\sf \mapsto \vec{A} . \vec{B} = (5 \hat{i} \: . \: 3 \hat{i} \: + \: 5 \hat{i} \: . \: 4 \hat{j}) + (6 \hat{j} \: . \: 3 \hat{i} \: + \: 6\hat{j} \: . \: 4 \hat{j}) + (8 \hat{k} \: . \: 3 \hat{i} \: + \: 8 \hat{k} \: . \: 4 \hat{j})$

$\mapsto \sf \vec{A}. \vec{B} = (0 + 20) + (24 + 0) + (24 + 32)$

$\: \therefore \: { \underline{ \boxed{ \sf \vec{A}. \vec{B} = 100}}}$

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