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Three Dimensional Geometry

Question

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What is the cosine of the angle which the vector $\sqrt{2} \hat{i} + \hat{j} + k$ makes with y-axis?

Solution

The y-axis can be represented in vector form by $\hat{j} and - \hat{j} .$

$Let \vec{a} = \sqrt{2} \hat{i} + \hat{j} + k and \vec{b} = \hat{j} or - \hat{j} cosθ = \frac{\hat{a} . b}{|\hat{a}| |b|} ∴ cosθ = \frac{(\sqrt{2} \hat{i} + \hat{j} + k) . (\pm \hat{j})}{|\sqrt{2} \hat{i} + \hat{j} + k| . |\hat{j}|} = \pm \frac{1 x 1}{\sqrt{{(\sqrt{2})}^{2} + {(1)}^{2} + {(1)}^{2}} x \sqrt{1^{2}}} = \pm \frac{1}{\sqrt{4}} = \pm \frac{1}{2} So, the cosine of the angle which the vector \sqrt{2} \hat{i} + \hat{j} + k makes with y - axis is \pm \frac{1}{2}$

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Three Dimensional Geometry

What is the cosine of the angle which the vector $\sqrt{2} \hat{i} + \hat{j} + k$ makes with y-axis?

Some More Questions From Three Dimensional Geometry Chapter

Find the direction cosines of x, y and z-axis.

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For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

What is the cosine of the angle which the vector 2 i^ + j^ + k makes with y-axis?

Some More Questions From Three Dimensional Geometry Chapter

Find the direction cosines of x, y and z-axis.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

What is the cosine of the angle which the vector $\sqrt{2} \hat{i} + \hat{j} + k$ makes with y-axis?