A straight line $L$ on the $x y$ -plane bisects the angle between $O X$ and $O Y$ . What are the direction cosines of $L$ ?

(1 / \sqrt{2}, 1 / \sqrt{2}, 0)

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(1 / 2, \sqrt{3} / 2, 0)

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(0, 0, 1)

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(2 / 3, 2 / 3, 1 / 3)

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Solution

The correct option is A $(1 / \sqrt{2}, 1 / \sqrt{2}, 0)$
L makes an angle $\frac{π}{4}$ with X and Y axis and $\frac{π}{2}$
Therefore, d.cs are $(cos \frac{π}{4}, cos \frac{π}{4}, cos \frac{π}{2}) = (\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0)$

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Similar questions

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are.

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\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}

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If $l_{1}, m_{1}, n_{1}, l_{2}, m_{2}, n_{2} a n d l_{3}, m_{3}, n_{3}$ are the direction cosines of three mutually perpendicular lines,then prove that the line whose direction cosines are proportional to $l_{1} + l_{2} + l_{3}, m_{1} + m_{2} + m_{3} a n d n_{1} + n_{2} + n_{3}$ makes equal angles with them.

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A straight line L on the xy-plane bisects the angle between OX and OY. What are the direction cosines ofL?

The correct option is A (1/√2,1/√2,0)L makes an angle π4 with X and Y axis and π2Therefore, d.cs are (cosπ4,cosπ4,cosπ2)=(1√2,1√2,0)

A straight line $L$ on the $x y$ -plane bisects the angle between $O X$ and $O Y$ . What are the direction cosines of $L$ ?

The correct option is A $(1 / \sqrt{2}, 1 / \sqrt{2}, 0)$
L makes an angle $\frac{π}{4}$ with X and Y axis and $\frac{π}{2}$
Therefore, d.cs are $(cos \frac{π}{4}, cos \frac{π}{4}, cos \frac{π}{2}) = (\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0)$