Home
Class 12
MATHS
The moment of the couple consisting of t...

The moment of the couple consisting of the force through the point `2hati -3hatj -hatk` is

A

5

B

`5sqrt5`

C

`sqrt5`

D

25

Text Solution

Verified by Experts

The correct Answer is:
B
Let A and B be the points having position vectors
` hati - hatj + hatk and 2hati -3hatj -hatk` respectively, then
`vecr = vec(BA) = (hati -hatj +hatk) - ( 2hati -3hatj -hatk) = - hati + 2hatj + 2hatk`
Let `vecM` b the moment of the couple. Then,
` vecM = vecr xx vecF |{:(hati, hatj ,hatk),(-1,2,2),( 3,2,-1):}| = -6 hati +5hatj -8hatk`
Moment fo the couple = ` |vecM|= sqrt(36+25+ 64) = 5sqrt5`
Promotional Banner

Topper's Solved these Questions

  • SCALER AND VECTOR PRODUCTS OF TWO VECTORS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|12 Videos

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA|Exercise Exercise|65 Videos

  • SOLUTIONS OF TRIANGLES

    OBJECTIVE RD SHARMA|Exercise Exercise|20 Videos

Similar Questions

Explore conceptually related problems

Find the vector equation of the plane passing through the point hati + hatj -2hatk and hati + 2hatj + hatk, 2hati - hatj + hatk.

The moment of the couple formed by the forces 5hati +hatj and -5hati - hatk acting at the points (9 ,-1,2) and ( 3,-2,1) respectively, is

Find the vector equation of the line passing through the point 2 hati + hatj - 3 hatk and perpendicular to the vectors hati + hatj + hatk and hati + 2 hatj - hatk .

The vector equation of the plane passing through the points hati+hatj-2hatk,2hati-hatj+hatk and hati+hatj+hatk , is

The position vector of the point in which the line joining the points hati-2hatj+hatk and 3hatk-2hatj cuts the plane through the origin and the points 4hatj and 2hati+hatk is

Find the equation of the plane passing through the point hati-hatj+hatk and perpendicular to the vectro 3hati-hatj-2hatk and show that the point 2hati+4hatj lies on the plane.

Find the vector equation of the plane passing through the point (3hati+4hatj+2hatk) and parallel to the vectors (hati+2hatj+3hatk) and (hati-hatj+hatk) .

Forces 2hati+hatj, 2hati-3hatj+6hatk and -hati+2hatj-hatk act at a point P, with position vector 4hati-3hatj-hatk . Find the vector moment of the resultant of these forces about thepoint Q whose position vector is 6hati+hatj=3hatk

The vector equation of a line passing through the point hati + 2hatj + 3hatk and perpendicular to the vectors hati +hatj + hatk and 2hati - hatj + hatk is