Home
Class 12
MATHS
The length of projection of the line ...

The length of projection of the line segment joining the points `(1,0,-1)a n d(-1,2,2)` on the plane `x+3y-5z=6` is equal to a. `2` b. `sqrt((271)/(53))` c. `sqrt((472)/(31))` d. `sqrt((474)/(35))`

Text Solution

Verified by Experts

The correct Answer is:
`3`
Let `A(1, 0, -1), B(-1, 2, 2)`
Direction ratios of `AB` are `(2, -2, -3)`
Let `theta` be the angle between the line and normal to plane , then
`" "costheta= (|2.1+ 3(-2)-5(-3)|)/(sqrt(1+9+25)sqrt(4+4+9))`
`" "= (11)/(sqrt(17)sqrt(35))= (11)/(sqrt(595))`
Length of projection
`" "=(AB) sin theta`
`" "= sqrt((2)^(2)+ (2)^(2)+ (3)^(2))xxsqrt(1- (121)/(595))`
`" "= sqrt((474)/(35))` units
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES SUBJECTIVE TYPE|5 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES SINGLE CORRECT ANSWER TYPE|9 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|5 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Archives (Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

The length of projection of the line segment joining the points (1,0,-1) and (-1,2,2) on the plane x+3y-5z=6 is equal to

The length of projection of the line segment joining the points (1,0,-1) and (-1,2,2) on the plane x+3y-5z=6 is equal to a. 2 b. sqrt((271)/(53)) c. sqrt((472)/(31)) d. sqrt((474)/(35))

The length of projection, of the line segment joining the points (1,-1,0) and (-1,0,1) to the plane 2x+y+6z=1 is equal to

The length of the projection of the line segment joining the points (5,-1,4) and (4,-1,3) on the plane x+y+z=7 is

The projection of the line segment joining the Points (1, 2, 3) and (4, 5, 6) on the plane 2x + y + z = 1 is

If the length of the projection of the line segment joining the points (1, 2, -1) and (3, 5, 5) on the plane 3x-4y+12z=5 is equal to d units, then the value of 169d^(2) equal to

The projection of the line segment joining the points A(-1,0,3) and B(2,5,1) on the line whose direction ratios are proportional to 6,2,3 is

Find the angle between the line joining the points (3,\ -4,\ -2)a n d\ (12 ,\ 2,\ 0) and the plane 3x-y+z=1.

The length of projection of the line segment joinint (3,-1,0) and (-3,5,sqrt(2)) on a line with direction cosiens 1/2,1/2,1/sqrt(2) is (A) 1 (B) 2 (C) 3 (D) 4

If tan(cos^(-1)x)="sin"(cot^(-1)(1/2)) then x is equal to- a. 1/sqrt(5) b. 2/sqrt(5) c. 3/sqrt(5) d. sqrt(5)/3