Question

A parallelogram is formed by two vectors as adjacent sides sweeping an area 15 square units. Find the area of triangle formed by the same two vectors (in sq units) ​

Answer 1

Given:

A parallelogram is formed by two vectors as adjacent sides sweeping an area 15 square units.

To find:

Area enclosed by the triangle formed by the vectors.

Calculation:

We will use congruency to find out the required area.

In ∆ABC and ∆ADC :

1. AB = DC [ Same magnitude of parallel vector]

2. BC = AD [Same magnitude of parallel vector]

3. AC is common line.

Hence , we can say :

$\boxed{ \bold{\Delta ABC \: \approx \: \Delta ADC \: ......(SSS)}}$

We know that congruent triangles have equal area.

∆ABC + ∆ADC = 15

=> 2 ∆ABC = 15

=> ∆ABC = 15/2

=> ∆ABC = 7.5 sq. units

Hence final answer is:

Area enclosed by vector triangle is 7.5 sq. units