Find the value of a so that the volume o...

Find the value of `a` so that the volume of the parallelepiped formed by vectors ` hat i+a hat j+k , hat j+a hat ka n da hat i+ hat k` becomes minimum.

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

The value of a so that the volume of parallelepiped formed by hat i+a hat j+ hat k , hat j+a hat k and a hat i+ hat k is minimum is a. -3 b. 3 c. 1//sqrt(3) d. sqrt(3)

Find the area of the parallelogram determined by the vectors: 2 hat i+ hat j+3 hat k\ a n d\ hat i- hat j

Find the area of the parallelogram determined by the vectors: hat i-3 hat j+ hat k\ a n d\ hat i+ hat j+ hat kdot

Find the area of the parallelogram determined by the vectors: 3 hat i+ hat j-2 hat k\ a n d\ hat i-3 hat j+4 hat k

Find the volume of a parallelepiped whose edges are given by -3 hat i+7 hat j-5 hat k ,-5 hat i+7 hat j- 3 hat ka n d7 hat i-5 hat j-3 hat kdot

Write the value of [ hat i+ hat j\ hat j+ hat k\ hat k+ hat i]

Write the value of [ hat i- hat j\ hat j- hat k\ hat k- hat i]

Find the value of lambda so that the following vectors are coplanar: vec a= hat i- hat j+ hat k , vec b=2 hat i+ hat j- hat k , vec c=lambda hat i- hat j+lambda hat k

Find the value of lambda if the volume of a tetrashedron whose vertices are with position vectors hat i-6 hat j+10 hat k ,- hat i-3 hat j+3 hat k ,5 hat i- hat j+lambda hat ka n d7 hat i-4 hat j+7 hat k is 11 cubic unit.

Find the values of x, y and z so that the vectors vec a=x hat i+2 hat j+z hat k and vec b=2 hat i+y hat j+ hat k are equal.

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions

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 parallelepiped whose three coterminous edtge...
Text Solution
|
If vec a and vec b are two vectors such that | vec a|=2, |vecb|=3 and...
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 r. vec a=0, vec r. vec b=1 \ and \ [[ vec r ,vec a, vec b]]=1,...
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 xxx vec a+( vec xdot 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
|
Let vec a , vec b and vec c be three non-zero vectors such that ve...
Text Solution
|
Prove that ( vec a.hat i)( vec axx hat i)+( vec a.j)( vec axx hat j)+(...
Text Solution
|
If ( vec axx vec b)^2+( vec a.vec b)^2=144 and | vec a|=4, then find t...
Text Solution
|