The value of a so that the volume of p...

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)`

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

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.

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]

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

Show that the area of a parallelogram having diagonals 3 hat i+ hat j-2 hat k\ a n d\ hat i-3 hat j+4 hat k is 5sqrt(3) square units.

Evaluate the following: [ hat i\ hat j\ hat k]+[ hat j\ hat k\ hat i]+[ hat k\ hat i\ hat j] .

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i- hat k) are collinear.

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.

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions

Volume of parallelepiped formed by vectors vec axx vec b , vec bxx...
Text Solution
|
Given three vectors vec a , vec b ,a n d vec c two of which are non-c...
Text Solution
|
The value of a so that the volume of parallelepiped formed by hat i...
Text Solution
|
A1,A2,..., An are the vertices of a regular plane polygon with n sides...
Text Solution
|
If c is a given non-zero scalar, and vec A and vec(B) are given ...
Text Solution
|
A , B , Ca n dD are any four points in the space, then prove that |...
Text Solution
|
[ veca + vecb vecb + vecc vecc + veca ]=[ veca vecb ...
Text Solution
|
Let vec A=2 vec i+ vec k , vec B= vec i+ vec j+ vec kdot vec C = 4hat...
Text Solution
|
Determine the value of c so that for all real x , vectors c x hat i-6 ...
Text Solution
|
If vec r=x1( vec axx vec b)+x2( vec bxx vec a)+x3( vec cxx vec a) and...
Text Solution
|
[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)(...
Text Solution
|
If V be the volume of a tetrahedron and V ' be the volume of another...
Text Solution
|
Let vec a , vec ba n d vec c be three non-coplanar vecrors and ve...
Text Solution
|
A(veca),B(vecb),C(vecc) are the vertices of the triangle ABC and R(vec...
Text Solution
|
Let vec a , vec ba n d vec c be three non-coplanar vectors and v...
Text Solution
|
Let vec a , vec ba n d vec c be three non-coplanar vecrors and ve...
Text Solution
|
The position vectors of point A ,B ,a n dC are hat i+ hat j+ hat k...
Text Solution
|
Let vec a(x)=(sin x) hat i+(cosx) hat j a n d vec b(x)=(cos2x) hat i+...
Text Solution
|
If vec a=2 hat i+ hat j+ hat k , vec b= hat i+2 hat j+2 hat k , vec c...
Text Solution
|
If vec a , vec ba n d vec c are unit vectors satisfying | vec a- v...
Text Solution
|