Home
Class 12
MATHS
Find the volume of the parallelopiped wh...

Find the volume of the parallelopiped whose cotermius edges are `2hat(i)+hat(j)+3hat(k),-hat(i)+2hat(j)+hat(k) and 3hat(i)+hat(j)+2hat(k)`.

Text Solution

Verified by Experts

Let `vec (a) = 2 hat(i) +hat(j) +3hat(k) vec( b) =- hat(i) +2hat(j)+hat(k) vec( c) =3hat(i) +hat(j)+2hat(k)`
Volume of parallelopiped `=[ vec (a) , vec( b) ,vec( c ) ] =|(2,1,3),(-1,2,1),(3,1,2)|=-10` sq units.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • VECTOR ALGEBRA

    SUBHASH PUBLICATION|Exercise TRY YOURSELF|4 Videos

  • VECTOR ALGEBRA

    SUBHASH PUBLICATION|Exercise TRY YOURSELF|4 Videos

  • TRIANGLES

    SUBHASH PUBLICATION|Exercise Exercise 5.7|1 Videos

Similar Questions

Explore conceptually related problems

Find the sum of vectos a = hat(i)- 2hat(j)+hat(k),b=-2hat(i)+4hat(j)+5hat(k) and c=hat(i)-6hat(j)-7hat(k) .

Find the area of the parallelogram whose adjacent sides are determined by the vectors a=hat(i)-hat(j)+3hat(k) and b=2hat(i)-2hat(j)+5hat(k) .

Knowledge Check

  • The area of the parallelogram whose adjacent sides are hat(i)+hat(k) and 2 hat(i)+hat(j)+hat(k) is

    A
    3
    B
    `sqrt(2)`
    C
    4
    D
    `sqrt(3)`

  • The value of p such that the vectors hat(i) + 3hat(j) - 2hat(k), 2hat(i) - hat(j) + 4hat(k) and 3hat(i) + 2hat(j) + p hat(k) are coplanar is

    A
    4
    B
    2
    C
    8
    D
    10

    • Similar Questions

    Explore conceptually related problems

    Find the vector equation of the plane passing through three points with position vectors (hat(i) + hat(j) - 2 hat(k)),(2 hat(i) - hat(j) + hat(k)) and (hat(i) + 2 hat(j) + hat(k)) . Also find the coordinates of the point of intersection of this plane and the line vec(r) = (3 hat(i) - hat(j) - hat(k)) + lambda (2 hat(i) - 2 hat(j) + hat(k)) .

    Find the value of lambda , if the point with position vectors 3hat(i) - 2hat(j) - hat(k), 2hat(i) + 3hat(j) - 4hat(k), -hat(i) + hat(j) + 2hat(k) and 4hat(i) + 5hat(j) + lambda hat(k) are coplanar.

    The Area of the Parallelogram determined by the vectors hat(i) + 2hat(j) + 3hat(k), -3hat(i) -2hat(j) + hat(k) (in sq. unit) is

    Find the unit vector perpendicular to the plane ABC where the position vectors A, B and C are 2hat(i) - hat(j) + hat(k), hat(i) + hat(j) + 2hat(k) and 2hat(i) + 3hat(k) .

    Find the sine of the angle between the vectors hat(i) + 2 hat(j) + 2 hat(k) and 3 hat(i) + 2 hat(j) + 6 hat(k)

    Find the angle between the vectors hat(i)-2hat(j)+3hat(k) and 3hat(i)-2hat(j)+hat(k) .

    Home
    Profile