Prove that the four points 6 hat i-7 hat...

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.

Text Solution

AI Generated Solution

Topper's Solved these Questions

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

Similar Questions

Explore conceptually related problems

Show that the four points having position vectors 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k ,2 hat i-5 hat j+10 hat k are coplanar.

Show that the points having position vectors 6 hat i-7 hat j ,\ 16 hat i-19 hat j-4 hat k ,\ 3 hat j-6 hat k ,\ 2 hat i+5 hat j+10 hat k are not coplanar.

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.

Show that four points whose position vectors are 6 hat i-7 hat j ,\ 16 i-19 hat j-4 hat k ,\ 3 hat i-6 hat k ,\ 2 hat i-5 hat j+10\ hat k are coplanar.

The four points whose position vector are 6 hat i - 7 hat j,16 hat i - 29 hat j - 4 hat k, 3 hat j - 6 hat k, 2 hat i + 5 hat j + 10 hat k are coplanar

Prove that the points hat i- hat j ,4 hat i-3 hat j+ hat k and 2 hat i-4 hat j+5 hat k are the vertices of a right angled triangle.

Prove that the following vectors are coplanar: hat i+ hat j+ hat k ,\ 2 hat i+3 hat j- hat k\ a n d- hat i-2 hat j+2 hat k

If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are collinear, then

Prove that the following vectors are coplanar: 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k\ a n d\ 3 hat i-4 hat j-4 hat k

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions

i. Prove that the points vec a-2vec b+3vec c, 2vec a+3vec b-4vec ...
Text Solution
|
Check whether the given three vectors are coplanar or non-coplanar. -2...
Text Solution
|
Prove that the four points 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ...
Text Solution
|
If vec a and vec b are two non-collinear vectors, show that points l1...
Text Solution
|
Show, by vector methods, that the angularbisectors of a triangle are c...
Text Solution
|
Let vec A(t) = f1(t) hat i + f2(t) hat j and vec B(t) = g(t)hat i+g2(...
Text Solution
|
Find the least positive integral value of x for which the angle betwee...
Text Solution
|
If vectors vec a= hat i+2 hat j- hat k , vec b=2 hat i- hat j+ hat k ...
Text Solution
|
Find the values of lambda such that x ,y ,z!=(0,0,0) and ( hat i+ hat ...
Text Solution
|
A vector has component A1, A2a n dA3 in a right -handed rectangular Ca...
Text Solution
|
The position vectors of the point A ,B ,C and D are 3 hat i-2 hat j- h...
Text Solution
|
Let O A C B be a parallelogram with O at the origin andO C a diagonal....
Text Solution
|
In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley,...
Text Solution
|
Prove by vector method that the line segment joining the mid-points...
Text Solution
|
If the resultant of two forces is equal in magnitude to one of the ...
Text Solution
|
The axes of coordinates are rotated about the z-axis through an angle ...
Text Solution
|
Three coinitial vectors of magnitudes a, 2a and 3a meet at a point ...
Text Solution
|
If two side of a triangle are hat i+2 hat j and hat i+ hat k , then...
Text Solution
|
If in parallelogram ABCD, diagonal vectors are vec A C=2 hat i+3 ha...
Text Solution
|
Find the resultant of vectors vec a= hat i- hat j+2 hat k and vec b...
Text Solution
|