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Calculate the are of the triangle determ...

Calculate the are of the triangle determined by the two vectors `vec(A)=3hat(i)+4hat(j)` and `vec(B)=-3hat(i)+7hat(j).`

A

`33` `(unit)^2 `

B

`2/33` `(unit)^2 `

C

`11/2` `(unit)^2 `

D

`33/2` `(unit)^2 `

Text Solution

Verified by Experts

The correct Answer is:
D
We know thet the half of magnitude of the cross product of two vectors gives the area of the triangle.
`vec(A)xxvec(B)=|(hat(i), hat(j), hat(k)) ,(3,4,0), (-3 ,7 ,0)|`
`=hat(i)(0-0)-hat(j)(0-0)+hat(k)(21+12)=33hat(k)`
Taking magnitude `|vec(A)xxvec(B)|=sqrt(33^(2))=33`.
So area of triangle `=1/2|vec(A)xxvec(B)|=33/2sq.`unit.
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