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

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

A

`-3`

B

`3`

C

`(1)/(sqrt(3`

D

`sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:

C

Topper's Solved these Questions

PRODUCT OF VECTORS
ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|18 Videos
PROBABILITY
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos
PROPERTIES AND SOLUTION OF TRIANGLES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

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

Find the value of a so that the volume of the parallelepiped formed by vectors hat i+ahat j+k,hat j+ahat k and ahat i+hat k becomes minimum.

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

The value of p so that vectors 2hat i-hat j+hat k , hat i+2hat j-3hat k and 3hat i+phat j+5hat k are coplanar is

underset with a = 2hat i + hat j-3hat k, vec b = -hat i + hat j + 2hat k, vec c = 4hat i + 3hat k

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-3 hat k) are collinear.

If the vectors 3 hat i +3 hat j +9 hat k and hat i +a hat j +3 hat k are parallel, then a =

If theta is the angle between the vectors 2 hat i-2 hat j+4 hat k\ a n d\ 3 hat i+ hat j+2 hat k , then sintheta= 2/3 b. 2/(sqrt(7)) c. (sqrt(2))/7 d. sqrt(2/7)

hat i.(2hat j times3hat k)+hat j.(2hat k times3hat i)+hat k.(2hat i times3hat j) is equal to

Find the area of the parallelogram determined by the vectors: 2hat i and 3hat j2hat i+hat j+3hat k and hat i-hat j3hat i+hat j-2hat k and hat i-3hat j+4hat khat i-3hat j+hat k and hat i+hat j+hat k

ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)

If vec a , vec b and vec c are three non-zero, non coplanar vecto...
Text Solution
|
The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk an...
Text Solution
|
The value of a so that the volume of parallelepiped formed by hat ...
Text Solution
|
If vec a=( hat i+ hat j+ hat k), vec adot vec b=1a n d vec axx vec b=...
Text Solution
|
Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...
Text Solution
|
If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...
Text Solution
|
Let a= 2hat(i) -2hat(k) , b=hat(i) +hat(j) and c be a vectors suc...
Text Solution
|
If [axxb bxxc c xxa]=lambda[abc]^(2), then lambda is euqual to
Text Solution
|
Let hata and hatb be two unit vectors. If the vectors vecc=hata+2hatb ...
Text Solution
|
Let ABCD be a parallelogram such that vec AB = vec q,vec AD = vec p a...
Text Solution
|
1/sqrt(10)(3hatj + hatk) and vecb =(2hati +3hatj-6hatk), then the valu...
Text Solution
|
The vectors a and b are not perpendicular and c and d are two vectors ...
Text Solution
|
If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+ha...
Text Solution
|
Let veca =hatj-hatk and vecc =hati-hatj-hatk. Then the vector b satisf...
Text Solution
|
If the vectors veca=hati-hatj+2hatk.vecb=2hati+4hatj+hatk and veccc=la...
Text Solution
|
If vecu, vecv, vecw are non -coplanar vectors and p,q, are real numbe...
Text Solution
|
The vector vec a=""alpha hat i+2 hat j+""beta hat k lies in the pl...
Text Solution
|
If vecu and vecv are unit vectors and theta is the acute angle bet...
Text Solution
|
Let bar a= hat i+ hat j+ hat k ,""b= hat i- hat j+2 hat k and bar...
Text Solution
|
If (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc), Where veca, vecb and vecc a...
Text Solution
|