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  • For given vectors and find the unit vector in the direction of the vector .

Q.9  For given vectors, \vec a = 2 \hat i - \hat j + 2 \hat k and \vec b = - \hat i + \hat j - \hat k , find the unit vector in the direction of the vector  \vec a + \vec b.

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best_answer

Given

\vec a = 2 \hat i - \hat j + 2 \hat k

\vec b = - \hat i + \hat j - \hat k

Now,

\vec a + \vec b=(2-1)\hat i+(-1+1)\hat j+ (2-1)\hat k

\vec a + \vec b=\hat i+\hat k

Now a unit vector in the direction of \vec a + \vec b

\vec u= \frac{\vec a + \vec b}{\left |\vec a + \vec b \right |}=\frac{\hat i+\hat j}{\sqrt{1^2+1^2}}

\vec u= \frac{\hat i}{\sqrt{2}}+\frac{\hat j}{\sqrt{2}}

Posted by

Pankaj Sanodiya

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