Home
Class 12
MATHS
Statement 1: Let theta be the angle betw...

Statement 1: Let `theta` be the angle between the line `(x-2)/2=(y-1)/(-3)=(z+2)/(-2)` and the plane `x+y-z=5.` Then `theta=sin^(-1)(1//sqrt(51))dot` Statement 2: The angle between a straight line and a plane is the complement of the angle between the line and the normal to the plane. Which of the following statements is/are correct ?

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
c
`sin theta = |(2-3+2)/(sqrt(4+9+4)sqrt(3))|= (1)/(sqrt(51))`
Therefore, Statement 1 is true and Statement 2 is also true by definition.
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|12 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise MATRIX-MATCH TYPE|5 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|17 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-2)/(1)=(y+1)/(3)=(z-4)/(2) and the plane 3x-2y+4z=6 .

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

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

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

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

The angles between the lines (x-5)/(2)=(y-3)/(2)=(z)/(0) and x=5,y=8,z=6t is -

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

The angle between the lines (x-5)/(1)=(y-1)/(0)=(z-9)/(0) and 2x-1=5-2y=sqrt(2)z is -

The angle between the straight lines 2x-y+3=0 and x+2y+3=0 is-

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