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  • If vector a is equal to i plus j plus k , find a unit vector parallel to the vector .

Q7   If \vec a = \hat i + \hat j + \hat k , \vec b = 2 \hat i - \hat j + 3 \hat k \: \: and\: \: \vec c = \hat i - 2 \hat j + \hat k, find a unit vector parallel to the vector 2\vec a - \vec b + 3 \vec c.

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best_answer

Given in the question,

\vec a = \hat i + \hat j + \hat k , \vec b = 2 \hat i - \hat j + 3 \hat k \: \: and\: \: \vec c = \hat i - 2 \hat j + \hat k

Now,

let vector \vec V=2\vec a - \vec b + 3 \vec c

\vec V=2(\hat i +\hat j +\hat k) - (2\hat i-\hat j+3\hat k)+ 3 (\hat i-2\hat j+\hat k)

\vec V=3\hat i-3\hat j+2\hat k

Now, a unit vector in direction of \vec V

\vec u =\frac{3\hat i-3\hat j+2\hat k}{\sqrt{3^2+(-3)^2+2^2}}=\frac{3}{\sqrt{22}}\hat i-\frac{3}{\sqrt{22}} \hat j+\frac{2}{\sqrt{22}}\hat k

Now,

A unit vector parallel to \vec V 

\vec u =\frac{3}{\sqrt{22}}\hat i-\frac{3}{\sqrt{22}} \hat j+\frac{2}{\sqrt{22}}\hat k 

OR

-\vec u =-\frac{3}{\sqrt{22}}\hat i+\frac{3}{\sqrt{22}} \hat j-\frac{2}{\sqrt{22}}\hat k

Posted by

Pankaj Sanodiya

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