Question

If the volume of tetrahedron whose vertices are A(0, 1, 2), B(2, -3, 0), C(1, 0, 2) and D(-2,-3,lambda) is `7/3` cu.units, then the value of λ is ______.

पर्याय

• 1

• - 2

• 3

• 4

Answer 1

If the volume of tetrahedron whose vertices are A(0, 1, 2), B(2, -3, 0), C(1, 0, 2) and D(-2,-3,lambda) is `7/3` cu.units, then the value of λ is 3.

Explanation:

`bar"AB" = 2hat"i" - 4hat"j" - 2hat"k"`,

`bar"AC" = hat"i" - hat"j"`

`bar"AD" = -2hat"i" - 4hat"j" + (lambda - 2)hat"k"`

Volume of tetrahedron = `1/6 [bar"AB" bar"AC" bar"AD"]`

`=> 7/3 = 1/6 |(2,-4,-2),(1,-1,0),(-2,-4,lambda-2)|`

`=> 14 = 2(2 - lambda) + 4(lambda - 2) - 2(- 6)`

`=> lambda = 3`