Home
Class 12
PHYSICS
The sides of a parallelogram represented...

The sides of a parallelogram represented by vectors `p = 5hat(i) - 4hat(j) + 3hat(k)` and `q = 3hat(i) + 2hat(j) - hat(k)`. Then the area of the parallelogram is :

Text Solution

Verified by Experts

When `vecAandvecB` are the diagonals of a parallelogram, then its
Area `=(1)/(2)|vecAxxvecB|vecAxxvecB=|(hati,hatj,hatk),(5,-4,3),(3,-2,1)|=i|(-4,3),(-2,-1)|-j|(5,3),(3,-1)|+k|(5,-4),(3,-2)|`
`=hati{(-4)(-1)-(3)(-2)}-hatj{(5)(-1)-(3)(3)}+hatk{5)(-2)-(-4)(3)}=10hati+14hatj+2hatk`
`|vecAxxvecB|=sqrt((10)^(2)+(14)^(2)+(2)^2)=sqrt(300)` area of parallelogram `(1)/(2)|vecAxxvecB|(1)/(2)xx10sqrt(3)=5sqrt(3)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The diagonals of a parallelogram are given by the vectors (3 hat(i) + hat(j) + 2hat(k)) and ( hat(i) - 3hat(j) + 4hat(k)) in m . Find the area of the parallelogram .

Two adjacent sides of a parallelogram are respectively by the two vectors hat(i)+2hat(j)+3hat(k) and 3hat(i)-2hat(j)+hat(k) . What is the area of parallelogram?

Find the angle between the vectors 2 hat(i) - hat(j) - hat(k) and 3 hat(i) + 4 hat(j) - hat(k) .

If the sides AB and AD of a parallelogram ABCD are represented by the vector 2 hat(i) + 4 hat(j) - 5 hat(k) and hat(i) + 2 hat(j) + 3 hat(k) , then a unit vector along vec( AC ) is

If vector hat(i) - 3hat(j) + 5hat(k) and hat(i) - 3 hat(j) - a hat(k) are equal vectors, then the value of a is :

Find the angle between the vector vec(a) =2 hat(i) + 3hat(j) - 4 hat(k) and vec(b) = 4hat(i) +5 hat(j) - 2hat(k) .

Find the area of parallelogram whose adjacent sides are represented by the vectors 3hat(i)+hat(j)-2hat(k) and hat(i)-2hat(j)-hat(k) .

The adjacent sides of a parallelogram are hat(i) + 2 hat(j) + 3 hat(k) and 2 hat (i) - hat(j) + hat(k) . Find the unit vectors parallel to diagonals.

Projection of the vector 2hat(i) + 3hat(j) + 2hat(k) on the vector hat(i) - 2hat(j) + 3hat(k) is :

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :