Find a unit vector parallel to the resultant of the vectors $¯ A = 2^i + 3^J + 4^k$ and $¯ B = 3^i - 5^J$ .

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Solution

$Step 1: Calculate Resultant of two vectors$
$\to R = \to A + \to B$

$Step 2: Calculate unit vector parallel to$ $\to R$
$^R = \frac{\to R}{| \to R |}$

$\Rightarrow$ $^R = \frac{\to A + \to B}{| \to A + \to B |}$ $- - - - - - - - - - - - - - - - - - - (1)$

$Step 3:$ $Calculations$
$\to A + \to B = (2^i + 3^j + 4^k) + (3^i - 5^j)$

$\Rightarrow$ $\to A + \to B = 5^i - 2^j + 4^k$

$\Rightarrow$ $| \to A + \to B | = \sqrt{25 + 4 + 16}$

$= \sqrt{45}$
From equation $(1)$
$∴$ $^R = \frac{5^i - 2^j + 4^k}{\sqrt{45}}$
Unit vector parellel to resultant will be same as unit vector along resultant (because direction will be same)

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Find a unit vector parallel to the resultant of the vectors ¯A=2^i+3^J+4^k and ¯B=3^i−5^J.

Find a unit vector parallel to the resultant of the vectors $¯ A = 2^i + 3^J + 4^k$ and $¯ B = 3^i - 5^J$ .