Home
Class 12
MATHS
The position vectors of the four angular...

The position vectors of the four angular points of atetrahedronare `A(hat(j)+2hat(k)),B(3hat(i)+hat(k)),C(4hat(i)+3hat(j)+6hat(k))` and `D(2hat(i)+3hat(j)+2hat(k))` . Find the volume of the tetrahedron ABCD.

Text Solution

Verified by Experts

The correct Answer is:
`2` cubic unit
Promotional Banner

Similar Questions

Explore conceptually related problems

If 3hat(i) + 2hat(j) -5hat(k)= x(2hat(i) -hat(j) + hat(k)) + y(hat(i) + 3hat(j)-2hat(k))+z(-2hat(i) + hat(j)-3hat(k)) , then

If the vectors 4hat(i) + 11hat(j) + m hat(k), 7hat(i) + 2hat(j) + 6hat(k) and hat(i) + 5hat(j)+ 4hat(k) are coplanar, them m is equal to .

If the vectors vec(a) = 2hat(i) + hat(j) + 4hat(k), vec(b) = 4hat(i) - 2hat(j) + 3hat(k) and vec(c) = 2hat(i) - 3hat(j) - lambda hat(k) are coplanar, then findvalue of lambda

The point of intersection of the line vec(r)=7hat(i)+10hat(j)+13hat(k)+s(2hat(i)+3hat(j)+4hat(k)) and vec(r)=3hat(i)+5hat(j)+7hat(k)+t(hat(i)+2hat(j)+3hat(k)) is :

The straight line r = (hat(i) + hat(j) + hat(k)) + alpha (2hat(i) - hat(j) + 4hat(k)) meets the XY - plane at the point

The straight line r = (hat(i) + hat(j) + 2hat(k)) + t(2hat(i) + 5hat(j) + 3hat(k)) is parallel to the plane r.(2hat(i) + hat(j) - 3hat(k)) = 5 . Find distance between the straight line and plane