Question

Prove that the magnitude of area of the parallelogram formed by the adjacent side's of the Vectors A = 3i + 2j and B = 2i - 4j is ✓224 units.<br />please solve it friend

Answer 1

Hey!?


We know that Area of triangle ABC

∆=1/2*a*b*sin C

Here C is the angle between side a and b.

Let's A and B are the two adjacent sides of parallelogram PQRS.

We all know that in parallelogram PQRS area of triangle PQS and QRS are same.

So area of parallelogram PQRS=2 Times of area of triangle PQS.

Let QP=A=(2i+3j)

And QS=B=(i+4j)

So area of triangle PQS=1/2×|QP||QS|sin (Q)

=1/2×|QP×QS|=1/2|A×B|

Here A×B is cross product of vector A and B.

So area of parallelogram PQRS=2 Times of area of triangle PQS.

=|A×B|

I hope it's help you...!!!!


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