The vector projection of a vector 3-4- on y-axis is

As the multiple of ĵ in the given vector is zero therefore this vector lies in XZ plane and projection of this vector on y axis is zero. ...

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Standard XIII

Physics

Unit Vectors

The vector pr...

Question

The vector projection of a vector $3^i + 4^k$ on y-axis is

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Zero

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Solution

Step 1: Given that:
A vector, let $\to A$ = $3^i + 4^j$
Step 2: Formula and concept used:

The component of $\to A$ along $\to B$ = $A cos θ$
Thus,
The projection of $\to A$ along $\to B$ = $A cos θ .^B$
But, we know that;
$\to A . \to B = A B cos θ$
$\Rightarrow A cos θ = \frac{\to A . \to B}{B}$
Thus,
The projection of $\to A$ along $\to B$
$= \frac{(\to A . \to B)}{B} . \frac{\to B}{B}$
$\Rightarrow \frac{(\to A . \to B) . \to B}{B^{2}}$
The vector along Y- the axis, let $\to B$ = $^j$
Step 3: Calculation of projection of the given vector on Y-axis:
= $\frac{(3^i + 4^k) .^j}{1} .^^j$
= 0
(As, $^i .^j =^k .^j = 0$ )
Thus,
The projection of the given vector on Y-axis will be zero.

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The vector projection of a vector 3^i+4^k on y-axis is

The vector projection of a vector $3^i + 4^k$ on y-axis is