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Q.
The unit vector in the direction of the vector $a =\hat{ i }+\hat{ j }+2 \hat{ k }$ is
Vector Algebra
Solution:
Unit vector in the direction of given vector can be calculated by formula $\hat{a}=\frac{a}{|a|}$ where, $|a|=$ magnitude of given vector a.
Given, $ a=\hat{i}+\hat{j}+2 \hat{k} $ comparing with $x=a \hat{i}+b \hat{j}+c \hat{k}$, we get $a=1, b=1, c=2$
Magnitude of vector $a =| a |=\sqrt{a^2+b^2+c^2}$
$=\sqrt{1^2+1^2+2^2}=\sqrt{6}$
$\therefore$ The unit vector $\hat{a}$ in the direction of vector $a=\hat{i}+\hat{j}+2 \hat{k}$ is given by $\hat{a}=\frac{a}{|a|}=\frac{1}{\sqrt{6}}(\hat{i}+\hat{j}+2 \hat{k})$
$=\frac{1}{\sqrt{6}} \hat{i}+\frac{1}{\sqrt{6}} \hat{j}+\frac{2}{\sqrt{6}} \hat{k}$