Home
Class 12
MATHS
Find the angle between the line (x+1)/2...

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

A

`(pi)/(2)`

B

`(pi)/(4)`

C

`(pi)/(6)`

D

`sin^(-1)((8)/(21))`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `theta` be the angle between the line and the plane, we have
`a=2,b=3,c=6`
`anda_(1)=10,b_(1)=2,c_(1)=-11`
`:.sintheta=|{:(aa_(1)+b b_(1)+c c_(1))/(sqrt(a^(2)+b^(2)+c^(2))sqrt(a_(1)^(2)+b_(1)^(2)+c_(1)^(2))):}|`
`=|{:((2)(10)+(3)(2)+(6)(-11))/(sqrt(2^(2)+3^(2)+6^(2))sqrt(10^(2)+2^(2)+11^(2))):}|`
`=|{:(20+6-66)/(sqrt(49)*sqrt(225)):}|=|{:(-40)/(7.15):}|`
`rArr" "theta=sin^(-1)((8)/(21))`
Promotional Banner

Topper's Solved these Questions

  • PLANE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Practice exercise (Exercise 1) Topical problems (Coplanarity of two lines and distance of a point from a plane)|16 Videos

  • PLANE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Practice exercise (Exercise 2) Miscellaneous problems|44 Videos

  • PLANE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|9 Videos

  • PAIR OR STRAIGHT LINES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|13 Videos

  • PRACTICE SET 01

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

Similar Questions

Explore conceptually related problems

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

The angle between the line (x+1)/(2)=(y)/(3)=(z-3)/(-6) and the plane 10x + 2y + 11z=8 is

The acute angle between the line (x+1)/(2) = (y)/(3)= (z-3)/(6) and the plane 10 x + 2y -11z = 8 is

Find the angle between the line (x+1)/(2)=(3y+5)/(9)=(3-z)/(-6) and the plane 10x+2y-11z=3

Find the angle between the lines (x+1)/(2)=(y)/(3)=(z-3)/(6) and the planes 3x+y+z=7 .

(i) Find the angle between the line : (x + 1)/(2) = (y)/(3) = (z - 3)/(6) and the plane 10x + 12y - 11z = 3 (ii) Find the angle between the line : (x + 1)/(2) = (y -1)/(2) = (z -2)/(4) and the plane 2x + y - 3z + 4 =0 . (iii) Find the angle between the plane 2x + 4y - z = 8 and line (x - 1)/(2) = (2 - y)/(7) = (3z + 6)/(12) (iv) Find the angle between the line (x - 1)/(3) = (3 -y)/(-1) = (3z + 1)/(6) and the plane 3x - 5y + 2z = 10 .

The angle between the line x/2 = y/3 = z/4 and the plane 3 x + 2y -3z =4 is

Find the angle between the line (x-2)/3=(y+1)/-1=(z-3)/2 and the plane 3x+4y+z+5=0 .