Home
Class 12
MATHS
Find the angle between the line (x-1)...

Find the angle between the line `(x-1)/3=(y-1)/2=(z-1)/4` and the plane `2x+y-3z+4=0.`

Text Solution

Verified by Experts

The angle between a line and a plane is complement of the angle between the line and the normal of the plane, i.e., 3, 2, 4 and normal 2, 1, -3. Therefore,
`" "costheta=(6+2-12)/(sqrt(29)*sqrt(14))=-(4)/(sqrt(406))`
`" "theta=cos^(-1) (-4//sqrt(406))`
`" "phi=90^(@)-theta`
`" " = 90^(@)- cos^(-1) * (-4//sqrt(406))`
`" " = sin ^(-1) (-4//sqrt(406))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 3.4|5 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise SUBJECTIVE TYPE|17 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 3.2|15 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

Similar Questions

Explore conceptually related problems

Find the angle between the line (x-1)/(3)=(y+1)/(2)=(z+2)/(4) and the plane 2x+y-3z+4=0 .

Find the distance between the line (x+1)/(-3)=(y-3)/2=(z-2)/1 and the plane x+y+z+3=0.

Knowledge Check

  • The angle between the line (x-1)/(2)=(y-2)/(1)=(z+3)/(-1) and the plane x+y+4=0 is __

    A
    `45^(@)`
    B
    `60^(@)`
    C
    `30^(@)`
    D
    `75^(@)`

    • Similar Questions

    Explore conceptually related problems

    Find the angle between the line (x-2)/(1)=(y+1)/(3)=(z-4)/(2) and the plane 3x-2y+4z=6 .

    find the angle between the line (x+1)/2=y/3=(z-3)/6 and the plane is 10x+2y-11z=3

    If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the plane 2x-y+sqrt(pz)+4=0 is such that sintheta=1/3 , then the values of p is (A) 0 (B) 1/3 (C) 2/3 (D) 5/3

    If angle theta bertween the line (x+1)/1=(y-1)/2=(z-2)/2 and the plane 2x-y+sqrt(lambda)z+4=0 is such that sin theta=1//3, the value of lambda is a. -3/5 b. 5/3 c. -4/3 d. 3/4

    Find the angle between the lines 2x=3y=-z and 6x=-y=-4z

    Find the angle between the plane x-y+2z=9 and 2x+y+z=7

    Find the image of the line (x-1)/(9)=(y-2)/(-1)=(z+3)/(-3) in the plane 3x-3y+10z-26=0.

    Home
    Profile