Given A- -2- -3- and B- - - The component of vector A- along vector B- is-

The correct option is B 5 √( 2 ) Given: A⃗ = 2î + 3ĵ #160; #160; #160; #160; #160; #160; B⃗ = î + ĵ ⇒ |B⃗| #160; ...

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Byju's Answer

Standard XII

Physics

Comparing Vectors

Given A⃗ =2...

Question

Given $\to A = 2^i + 3^j$ and $\to B =^i +^j$ . The component of vector $\to A$ along vector $\to B$ is:

\frac{1}{\sqrt{2}}

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\frac{3}{\sqrt{2}}

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\frac{5}{\sqrt{2}}

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\frac{7}{\sqrt{2}}

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Solution

The correct option is B $\frac{5}{\sqrt{2}}$
Given: $\to A = 2^i + 3^j$
$\to B =^i +^j$

$\Rightarrow$ $| \to B | = \sqrt{1^{2} + 1^{2}} = \sqrt{2}$

$\to A . \to B = (2^i + 3^j) . (^i +^j) = 2 + 3 = 5$
Component of vector $\to A$ along vector $\to B$ is, $| \to X | = \frac{\to A . \to B}{| \to B |}$
$\Rightarrow | \to X | = \frac{5}{\sqrt{2}}$

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Given →A=2^i+3^j and →B=^i+^j. The component of vector →A along vector →B is:

The correct option is B 5√2Given: →A=2^i+3^j →B=^i+^j⇒ |→B|=√12+12=√2→A.→B=(2^i+3^j).(^i+^j)=2+3=5Component of vector →A along vector →B is, |→X|=→A.→B|→B|⇒|→X|=5√2

Given $\to A = 2^i + 3^j$ and $\to B =^i +^j$ . The component of vector $\to A$ along vector $\to B$ is: