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The vector in the direction of the vector $\hat i+2\hat j+2\hat k$ that has magnitude $9$ is

\begin{array}{1 1}(A)\;\hat i+2\hat j+2\hat k & (B)\;6(\hat i+2\hat j+2\hat k)\\(C)\;3(\hat i+2\hat j+2\hat k) & (D)\;9(\hat i+2\hat j+2\hat k)\end{array}
Can you answer this question?

Toolbox:
• Unit vector along $\overrightarrow a$ is $\large\frac{ \overrightarrow a}{| \overrightarrow a|}$
Let $\overrightarrow a=\hat i+2\hat j+2\hat k$
$|\overrightarrow a|=\sqrt{1^2+2^2+2^2}$
$\qquad=\sqrt9$
$\qquad=3$
Hence the vector in the direction of $\overrightarrow a$ is $\large\frac{\overrightarrow a}{|\overrightarrow a|}$
$=\Large\frac{\hat i+2\hat j+2\hat k}{3}$
The vector whose magnitude is 9 in the direction of $\overrightarrow a$ is
$=\Large\frac{9(\hat i+2\hat j+2\hat k)}{3}$
$=3(\hat i+2\hat j+2\hat k)$
Hence the correct option is $C$
answered May 28, 2013 by