Home
Class 12
PHYSICS
Find the area of the triangle formed by ...

Find the area of the triangle formed by the tips of the vectors `vec(a) = hati - hatj - 3hatk, vec(b) = 4hati - 3hatj +hatk` and `vec(c) = 3 hati - hatj +2 hatk`.

Text Solution

Verified by Experts


Let ABC is the triangle formed by the points A,B and C. Then
`bar(AB)=oversetrightarrow(B)-oversetrightarrow(A)=(4hati-3hatj+hatk)-(hati-hatj-3hatk)=3hati-2hatj+4hatk`
`bar(AC)=oversetrightarrow(C)-oversetrightarrow(A)=(3hati-3hatj+2hatk)-(hati-hatj-3hatk)=2hatj+4hatk`
`Now, oversetrightarrow(AB)xxoversetrightarrow(AB)=oversetrightarrow(A)=(3hati-2hatj+4hatk)xx(2hati+5hatk)`
`=i(-10-0)+hatj(8-15)+hatk(0+4)=-10hati-7hatj+4hatk`
Promotional Banner

Topper's Solved these Questions

  • CIRCULAR MOTION

    ALLEN|Exercise EXERCISE (S-1)|10 Videos

  • CIRCULAR MOTION

    ALLEN|Exercise Dynamics of circular motion|8 Videos

  • BASIC MATHS

    ALLEN|Exercise Question|1 Videos

  • CURRENT ELECTRICITY

    ALLEN|Exercise All Questions|427 Videos

Similar Questions

Explore conceptually related problems

Calculate the area of the triangle formed by the tips of vectors vecP=2hati+hatj-3hatk, vecQ=3hati-hatj+2hatk and vecR=4hati-3hatj+hatk

Find the area of the triangle formed by points O,A and B such that vec(OA) = hati + 2hatj + 3hatk and vec(OB) =- 3hati - 2hatj + hatk

Prove that the vectors vec(A) = 2hati - 3hatj - hatk and vec(B) =- 6 hati + 9hatj +3hatk are parallel.

Find the sine of the angle between the vectors vec(A) = 3 hati - 4hatj +5hatk and vec(B) = hati - hatj +hatk .

Find the angle between the vectors vec(A) = 2 hati - 4hatj +6 hatk and vec(B) = 3 hati + hatj +2hatk .

What is the projection of vec(A) = hati + hatj+ hatk on vec(B) = (hati + hatk)

Find the angle between the vertors vec(A) = hati + 2hatj - hatk and vec(B) = - hati +hatj - 2hatk .

Find the unit vector parallel to the resultant of the unit vectors vec(A) = 2 hati - 6 hatj - 3hatk and vec(B) = 4 hati +3hatj - hatk .

If vec(a) = hati - 2hatj - 3hatk, vec(b) = 2 hati - hatj - hatk and vec(c) = hati +3 hatj - 2hatk find (vec(a) xx vec(b)) xx vec(c)

Find the angle between the vectors vec A = hati + hatj + hatk and vec B =-hati - hatj + 2hatk .