A→ and B→ are two vectors given by A→$$=2i^+3j^$$ and B→$$=i^+j^$$. The magnitude of component of A→ along B→ $$is______$$

Magnitude of component of A→ along B→A $$cos$$θ$$=$$ A→ . B→B $$=$$ $$2+32$$ $$=52$$

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Question

$\vec{A} and \vec{B}$ are two vectors given by $\vec{A} = (2 \hat{i} + 3 \hat{j}) and \vec{B} = (\hat{i} + \hat{j}) .$ The magnitude of component of $\vec{A} along \vec{B} is$ ______

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Solution

Magnitude of component of $\vec{A} along \vec{B}$
$A cosθ = |(\frac{\vec{A} . \vec{B}}{B})| = |(\frac{2 + 3}{\sqrt{2}})| = \frac{5}{\sqrt{2}}$

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