Home
Class 12
MATHS
Find the angle between two planes given ...

Find the angle between two planes given by `3x+ 4y -5 z = 6 and 5x + 10 y - 20 z = 14`. Using
vector method.

Text Solution

Verified by Experts

The angle between two planes is gives by
`cos theta = (vecn_(1) cdot vecn_(2))/(abs(vecn_(1))abs(vecn_(2)))`
here `vecn_(1)=3hati + 4hatj - 5hatk`
`vecn_(2) = 5hati + 10hatj - 20hatk`
`cos theta = (15+ 40 + 100)/(sqrt(50) sqrt(400+100+25))`
`= 155/(5sqrt(2)sqrt(525))=155/(25sqrt(2)sqrt(21))`
`cos theta = 31/(5 sqrt(42))`
`theta = cos ^(-1) (31/(5sqrt42))`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise Illustration|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise TRY YOURSELF|97 Videos

  • STRAIGHT LINES

    AAKASH INSTITUTE|Exercise SECTION-J (AAKASH CHALLENGERS QUESTIONS)|5 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Section - J (Akash Challengers Question)|15 Videos

Similar Questions

Explore conceptually related problems

Find the angle between the planes 2x - y + 3z = 6 and x + y +2z =7 .

Find the angle between the planes 2x + y - 2z = 5 and 3x - 6y - 2z = 7 . Using vector method.

angle between two planes : 2x + y - 2z = 5 and 3x - 6y - 2z = 7 is sin^(-1) ((4)/(21))

Find the angle between the two planes 3x-6y+2z=7 and 2x+2y-2z=5

Find the angle between the planes 3x+y+2z=1 and 2x-y+z+3 = 0 .

Find the angle between the plane: 2x+y-2z=5 and 3x-6y-2z=7

Find the angle between the plane: 3x-6y+2z=7 and 2x+2y-2z=5

Find the angle between the plane: x-y+z=5\ a n d\ x+2y+z=9

Find the angle between the planes -x+y+2z=9 and x+2y+z=5

Distance between two planes : 2x + 3y + 4z = 5 and 4x + 6y + 8z = 12 is :