Home
Class 12
MATHS
A vector v is equally inclined to the X-...

A vector v is equally inclined to the X-axis, Y-axis and Z-axis respectively the dirction cosines are

A

`lt1/sqrt3,1/sqrt3,1/sqrt3gt`

B

`lt-1/sqrt3,1/sqrt3,-1/sqrt3gt`

C

`lt1/sqrt3,1/sqrt3,1/sqrt3gtorlt-1/sqrt3,-1/sqrt3,-1/sqrt3`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let the vector v makes an angle `alpha` with each of the three axes, then direction cosines of v are
`(cosalpha,cosalpha,cosalpha)`
Also, cos^2alpha+cos^2alpha+cos^2alpha=1`
rArr" "cos^2alpha=1/3`
`rArr" "cosalpha=pm1/sqrt3`
Hence, direction cosines of v are
`(1/sqrt3,1/sqrt3,1/sqrt3) or (-1/sqrt3,1/sqrt3,-1/sqrt3)`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (MISCELLANEOUS PROBLEMS)|22 Videos

  • STRAIGHT LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2(MISCELLANEOUS PROBLEMS)|30 Videos

  • TRIGONOMETRIC FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|26 Videos

Similar Questions

Explore conceptually related problems

A line makes 30^(@), 120^(@) and 90^(@) angles from the positive direction of x-axis, y-axis and pi -axis respectively. Find its direction cosines.

What are the direction cosines of Z-axis?

What are the direction cosines of z axis?

A line makes an obtuse angle with the positive X-axis and angle pi/4 and pi/3 with positive Y and Z-axes respectively. Its directions cosines are

Let a vector r make angles 60^(@), 30^(@) with X and Y -axis, respectively. What are the direction cosines of r ?

Q.A straight line is inclined to the axis of Y and Z at angle 45^(@) and 60^(@) respectively.the inclination of the line with the X-axis is

IF a unit vector veca makes angles pi/4 and pi/3 with x-axis and y-axis respectively and an acute angle theta with z-axis, then find theta and the (scalar and vector) coponents of veca along the axes.

What are the direction cosines of the y-axis ?

If a line OP through the origin O makes angles alpha,45^(@)and60^(@) with x, y and z axis respectively then the direction cosines of OP are.