If a- - 4- - 6- and b- - 3- - 4k- then the component of a- along b- is

The correct option is B 1825 (3#160;j + 4#160;k) Unit vector along b is b|b|=35ĵ+45k̂ Magnitude of a along b is a.b=185=m Henc ...

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Byju's Answer

Standard XII

Physics

Vector Addition

If a⃗ = 4î ...

Question

If $\to a = 4^i + 6^j$ and $\to b = 3^j + 4^k$ , then the component of $\to a$ along $\to b$ is

\frac{18}{10 \sqrt{3}} (3^j + 4^k)

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\frac{18}{25} (3^j + 4^k)

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\frac{18}{\sqrt{3}} (3^j + 4^k)

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(3^j + 4^k)

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Solution

The correct option is B $\frac{18}{25} (3^j + 4^k)$
Unit vector along $\to b$ is
$\frac{\to b}{| b |} = \frac{3}{5}^j + \frac{4}{5}^k$
Magnitude of $\to a$ along $\to b$ is
$\to a . ˆ b = \frac{18}{5} = m$
Hence component along $\to b$ is $m (ˆ b)$

$= \frac{18}{5} [\frac{3}{5}^j + \frac{4}{5}^k]$

$= \frac{18}{25} [3^j + 4^k]$

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If →a=4^i+6^j and →b=3^j+4^k, then the component of →a along →b is

The correct option is B 1825(3^j+4^k)Unit vector along →b is →b|b|=35^j+45^kMagnitude of →a along →b is →a.ˆb=185=mHence component along →b is m(ˆb)=185[35^j+45^k]=1825[3^j+4^k]

If $\to a = 4^i + 6^j$ and $\to b = 3^j + 4^k$ , then the component of $\to a$ along $\to b$ is