Maths-

General

Easy

Question

# The direction cosines of the line joining the points (4, 3, - 5) and (-2, 1, -8) are

- < 2, 4, -13 >
- < 6, 2, 3 >
- < 6/7, 2/7, 3/7 >
- None of these

Hint:

### We are given the coordinates of two points. We have to find the direction cosines of the line joining the two points. Direction cosines are the values of cosines of the given line. They are the cosines of angles it makes with the three axis.

## The correct answer is: < 6/7, 2/7, 3/7 >

### We will denote the given point by P and Q.

P = (4,3,-5)

Q = (-2,1,-8)

Direction cosines are denoted by l, m, and n.

To find the direction cosines, we take the difference between the coordinates and the distance between two points. It is the ratio of direction ratio and distance between the points.

We will find the distance between the given points using the distance formula.

Direction ratios are as follows:

x_{1} - x_{2 }= 4 - (-2)

= 4 + 2

= 6

y_{1} - y_{2} = 3 - 2

= 1

z_{1} - z_{2} = -5 - (-8)

= -5 + 8

= 3

ubstituting the values,

The direction cosines of the line joining two points are as follows:

For such questions, we should know formula to find direction cosines.

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