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State True or False for the given statement:

The unit vector normal to the plane x + 2y +3z - 6 = 0 is \frac{1}{\sqrt{14}}\hat{i}+\frac{2}{\sqrt{14}}\hat{j}+\frac{3}{\sqrt{14}}\hat{k}

Answers (1)

Given, the equation of the plane is x + 2y + 3z - 6 = 0

The normal to this plane will be \vec{n}=\hat{i}+2 \hat{j}+3\hat{k}

The unit vector of this normal is:

\\ \vec{n}=\frac{\vec{n}}{\left |\vec{n} \right |}\\ \vec{n}=\frac{\hat{i}+2\hat{j}+3\hat{k}}{\sqrt{1^{2}+2^{2}+3^{2}}}=\frac{1}{\sqrt{14}}\hat{i}+\frac{2}{\sqrt{14}}\hat{j}+\frac{3}{\sqrt{14}}\hat{k}

Therefore, the statement is True

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