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Q.

If vectors $\vec{A} and \vec{B} are 3 i - 4 j + 5 k and 2 i + 3 j - 4 k$ respectively. Find the unit vector parallel to $\vec{A} + \vec{B}$

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a

$\frac{(5 i - j + k)}{\sqrt{27}}$

b

$\frac{(5 i + j + k)}{\sqrt{27}}$

c

$\frac{(5 i + j + k)}{27}$

d

$\frac{(5 i - j - k)}{27}$

answer is A.

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Detailed Solution

detailed_solution_thumbnail

From the given vectors, $\vec{A} + \vec{B}$ is

$\vec{A} + \vec{B} =5i-j+k$

Unit vector along $\vec{A} + \vec{B}$ is

$\frac{\vec{A} + \vec{B}}{|\vec{A} + \vec{B}|} = \frac{5 i - j + k}{\sqrt{27}}$

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If vectors A→ and B→ are 3i−4j+5k and 2i+3j−4k respectively. Find the unit vector parallel to A→ +B→