Home
Class 12
MATHS
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 k and a hat i+ hat k` becomes minimum.

Text Solution

Verified by Experts

`V=|{:(1,a,1),(0,1,a),(a,0,1):}|=1-a+a^(3)`
`Rightarrow" " (dV)/(da)=3a^(2)-1`
V is minimum at a `=1/sqrt3`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.1|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.2|15 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 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

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

Find the area of the parallelogram whose Whose diagonals are the vectors 3 hat (i) + hat (j) - 2 hat (k) and hat (i) - 3 hat (j) + 4 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

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

Find the angle between the vectors vec a= hat i+hat j-hat k and vec b=hat i-hat j+hat k

Find the value of lambda for which the three points with position vector 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k , and4 hat i+5 hat j+lambda hat k are coplanar.

Find out the angle between two-vectors hat i + hat j and hat i- hat k .

Find the area of a parallelogram whose adjacent sides are given by the vectors vec a=3 hat i+ hat j+4 hat k and vec b= hat i- hat j+ hat k .

The , perpendicular vector on both of (3hat i +hat j + 2hat k) and (2hat i -2hat j +4hat k) is: