What will be the projection of vector A-k- on vector B- -

The projection of A on B is given by, (|A| cos θ)B̂=(A.B|B|)B̂ =1+1+0√(1^2+1^2)i+j√(1^2+1^2) =2√(2)(î+ĵ√(2))=î+ĵ Hence, (D) is the correct answer. ...

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Standard XII

Physics

Summary

What will be ...

Question

What will be the projection of vector $\to A =^i +^j +^k$ on vector $\to B =^i +^j ?$

\sqrt{2} (^i +^j +^k)

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\sqrt{2} (^i +^j)

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(^i +^j)

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2 (^i +^j +^k)

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Solution

The correct option is C $(^i +^j)$
The projection of $\to A$ on $\to B$ is given by,

$(| \to A | cos θ)^B = ⎛ ⎜ ⎝ \frac{\to A . \to B}{| \to B |} ⎞ ⎟ ⎠^B$

$= \frac{1 + 1 + 0}{\sqrt{1^{2} + 1^{2}}} \frac{i + j}{\sqrt{1^{2} + 1^{2}}}$

$= \frac{2}{\sqrt{2}} (\frac{^i +^j}{\sqrt{2}}) =^i +^j$

Hence, $(D)$ is the correct answer.

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

The correct option is C (^i+^j)The projection of →A on →B is given by, (|→A| cos θ)^B=⎛⎜⎝→A.→B|→B|⎞⎟⎠^B =1+1+0√12+12i+j√12+12 =2√2(^i+^j√2)=^i+^j Hence, (D) is the correct answer.

What will be the projection of vector $\to A =^i +^j +^k$ on vector $\to B =^i +^j ?$