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Standard XII

Mathematics

Direction Cosines

If Px, y, z...

Question

If $P (x, y, z)$ is point in the space at a distance $r$ from the origin $O$ , then direction cosines of the line $O P$ are

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Solution

Given $| O P | = r$ , where $O (0, 0, 0)$ is the origin and $P (x, y, z)$ be any point in the space.
Now direction cosines of $O P$ is $(\frac{x - 0}{| O P |}, \frac{y - 0}{| O P |}, \frac{z - 0}{| O P |})$ $= (\frac{x}{r}, \frac{y}{r}, \frac{z}{r})$ .

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Similar questions

Assertion $(A)$ . The direction ratios of the line joining origin and point $(x, y, z)$ must be $x, y, z$

Reason (R): lf $P (x, y, z)$ is a point in space and $| O P | = r,$ then the direction cosines of $O P$ are $\frac{x}{r}$ , $\frac{y}{r}$ , $\frac{z}{r}$

Q. In a line

O P

through the origin

O

makes angles of

90^{\circ}, 60^{\circ} a n d 60^{\circ}

with

x, y

and

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If a line OP through the origin O makes angles of $30^{o}$ , $45^{\circ}$ and $60^{\circ}$ with $x, y a n d z$ axis respectively then the direction cosines of OP are

Q. If the direction cosines of the line joining the origin and a point at unit distance from the origin are

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

- \frac{1}{2}

λ

then value of

λ

is?

Q. Find the direction cosines (d.cs) of directed line

O P

if coordinates of

P

(2, 3, 7)

O

being the origin.

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If P(x,y,z) is point in the space at a distance r from the origin O, then direction cosines of the line OP are

Given |OP|=r, where O(0,0,0) is the origin and P(x,y,z) be any point in the space.Now direction cosines of OP is (x−0|OP|,y−0|OP|,z−0|OP|)=(xr,yr,zr).

If $P (x, y, z)$ is point in the space at a distance $r$ from the origin $O$ , then direction cosines of the line $O P$ are

Given $| O P | = r$ , where $O (0, 0, 0)$ is the origin and $P (x, y, z)$ be any point in the space.
Now direction cosines of $O P$ is $(\frac{x - 0}{| O P |}, \frac{y - 0}{| O P |}, \frac{z - 0}{| O P |})$ $= (\frac{x}{r}, \frac{y}{r}, \frac{z}{r})$ .