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Q6   Find a vector of magnitude 5 units, and parallel to the resultant of the vectors \vec a = 2 \hat i + 3 \hat j - \hat k \: \: and \: \: \vec b = \hat i - 2 \hat j + \hat k

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Given two vectors 

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

Resultant of \vec a and \vec b:

\vec R = \vec a +\vec b=2 \hat i + 3 \hat j - \hat k + \hat i - 2 \hat j + \hat k=3\hat i + \hat j

Now, a unit vector in the direction of \vec R

\vec u =\frac{3\hat i+\hat j}{\sqrt{3^2+1^2}}=\frac{3}{\sqrt{10}}\hat i+\frac{1}{\sqrt{10}}\hat j

Now, a unit vector of magnitude in direction of\vec R

 \vec v=5\vec u =5*\frac{3}{\sqrt{10}}\hat i+5*\frac{1}{\sqrt{10}}\hat j=\frac{15}{\sqrt{10}}\hat i+\frac{5}{\sqrt{10}}\hat j

Hence the required vector is \frac{15}{\sqrt{10}}\hat i+\frac{5}{\sqrt{10}}\hat j.

 

Posted by

Pankaj Sanodiya

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