The position vectors of the four angu...

The position vectors of the four angular points of a tetrahedron are `A( hat j+2 hat k),B(3 hat i+ hat k), C(4 hat i+3 hat j+6 hat k)a n dD(2 hat i+3 hat j+2 hat k)dot` Find the volume of the tetrahedron `A B C Ddot`

Topper's Solved these Questions

TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS
CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos
VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS
CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

find the projection of 3hat i - hat j + 4hat k on 2 hat i + 3 hat j -6 hat k

Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k and 2 hat i + 5 hat j - hat k from a triangle in space.

In each of the following show that the given vectors are coplanar: 4 hat (i) + 2 hat (j) + hat (k) , 2 hat (i) - hat (j) + 3 hat (k) , 8 hat (i) + 7 hat (k)

Prove that the four points 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k and 2 hat i+5 hat j+10 hatk form a tetrahedron in space.

Show that the vectors are mutually perpendicular hat (i) + 2 hat (j) + hat (k) ,hat (i) + hat (j) - 3 hat (k) and 7 hat (i) - 4 hat (j) + hat (k)

The position vectors of the point A ,B ,C and D are 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k ,- hat i+ hat j+2 hat k and 4 hat i+5 hat j+lambda hat k , respectively. If the points A ,B ,C and D lie on a plane, find the value of lambda .

Find the vector of length 3 unit which is perpendicular to hat i+ hat j+ hat k and lies in the plane of hat i+ hat j+ hat k and 2 hat i-3 hat j .

If vec a= 2 hat i- hat j+ hat k and vec b = - hat i+3 hat j+4 hat k ,then veca.vecb =

Find the area of triangle whose vertices have position vectors hat (i) + hat (j) + 2 hat (k) , 2 hat (i) + 2 hat (j) + 3 hat (k) and 3 hat (i) - hat (j) - hat (k)

Find | -> axx -> b|, if -> a=2 hat i+ hat j+3 hat k and -> b=3 hat i+5 hat j-2 hat k .

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, ve...
Text Solution
|
Let A,B,C be three unit vectors and A.B= A.C=0. If the angle between ...
Text Solution
|
The position vectors of the four angular points of a tetrahedron ar...
Text Solution
|
If the vectors 2 hat i-3 hat j , hat i+ hat j- hat ka n d3 hat i- hat ...
Text Solution
|
If vec u , vec v and vec w are three non-coplanar vectors, then pro...
Text Solution
|
Find the value of a so that the volume of the parallelepiped formed ...
Text Solution
|
If vec a=2 hat i+3 hat j-5 hat k , vec b=m hat i+n hat j+12 hat k and...
Text Solution
|
Prove that [ vec l vec m vec n][ vec a vec b vec c]=| (vec l. vec a, v...
Text Solution
|
Find the altitude of a parallelopiped whose three coterminous edges ...
Text Solution
|
If veca and vecb are two vectors such that |veca|=2,|vecb|=3 and veca....
Text Solution
|
Prove that vec R+([ vec Rdot( vecbetaxx( vecbetaxx vecalpha))] vecalp...
Text Solution
|
If vec a , vec b ,and vec c are non-coplanar unit vectors such that...
Text Solution
|
If | vec a|=5,| vec a- vec b|=8 and | vec a+ vec b|=10 , then find | v...
Text Solution
|
If vec a and vec b are two given vectors and k is any scalar, then fi...
Text Solution
|
vec a , vec ba n d vec c are three non-coplanar ,non-zero vectors an...
Text Solution
|
If vector vec x satisfying vec x xx vec a+( vec x . vec b) vec c= ve...
Text Solution
|
Let hat a , hat b ,and hat c be the non-coplanar unit vectors. The...
Text Solution
|
Find the vector of length 3 unit which is perpendicular to hat i+ h...
Text Solution
|
If vec b is not perpendicular to vec c , then find the vector vec r...
Text Solution
|
If vec a , vec ba n d vec c are three non coplanar vectors, then ( ...
Text Solution
|