# Q.10  Find a vector in the direction of vector$5 \hat i - \hat j + 2 \hat k$ which has magnitude 8 units.

P Pankaj Sanodiya

Given a vector

$\vec a=5 \hat i - \hat j + 2 \hat k$

the unit vector in the direction of  $5 \hat i - \hat j + 2 \hat k$

$\vec u=\frac{5\hat i - \hat j + 2 \hat k}{\sqrt{5^2+(-1)^2+2^2}}=\frac{5\hat i}{\sqrt{30}}-\frac{\hat j}{\sqrt{30}}+\frac{2\hat k}{\sqrt{30}}$

A vector in direction of $5 \hat i - \hat j + 2 \hat k$ and whose magnitude is 8 =

$8\vec u=\frac{40\hat i}{\sqrt{30}}-\frac{8\hat j}{\sqrt{30}}+\frac{16\hat k}{\sqrt{30}}$

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