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Write a unit vector in the direction of \( \overrightarrow a = 2\hat i - 6\hat j + 3\hat k.\)

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  • Unit vector for a given vector $\overrightarrow a$ is $\hat n=\large\frac{\overrightarrow a}{\mid \overrightarrow a \mid}$
  • $\mid \overrightarrow a\mid=\sqrt{a_1^2+a_2^2+a_3^2}$
Step 1:
Given $\overrightarrow a=2\hat i-6\hat j+3\hat k$
$\mid\overrightarrow a\mid =\sqrt{(2)^2+(-6)^2+(3)^2}$
Step 2:
$\therefore$ unit vector along $\overrightarrow a$ is $\large\frac{1}{7}$$(2\hat i-6\hat j+3\hat k)$
answered Sep 21, 2013 by sreemathi.v

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