Question

If vectors A and B be respectively equal to 3hati - 4hatj + 5hatk and 2hati + 3hatj - 4hatk. Find the unit vector parallel t A + B

Answer 1

Unit vector parallel to A + B= $\frac{5\hat i - 1\hat j + 1\hat k}{\sqrt{27} }$

Given:

If vectors A and B be respectively equal to $3\hat i - 4\hat j + 5\hat k$ and $2\hat i + 3\hat j - 4\hat k.$

To find:

Unit vector parallel to A + B

Explanation:

Vector can be added or subtracted by unit quantity that is i can be added only i and j can be added only j so on.

   A + B = ($3\hat i - 4\hat j + 5\hat k$) +( $2\hat i + 3\hat j - 4\hat k.$)

   A + B =  $3\hat i - 4\hat j + 5\hat k$ + $2\hat i + 3\hat j - 4\hat k.$

             = $5\hat i - 1\hat j + 1\hat k$

Magnitude of vector = $\sqrt{5^2+1^2+1^2}$ = $\sqrt{27}$

Unit vector = $\frac{Full \ vector }{magnitude of vector}$

Unit vector parallel to A + B= $\frac{5\hat i - 1\hat j + 1\hat k}{\sqrt{27} }$

To learn more...

1)Convert the vector r = 3i + 2j into a unit vector.

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2)If A-ai +0.5j +0.5K is unit vector, then value of

'a' would be.

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