Find the area of triangle whose two sides are represented by the vectors 3i + 4j and 5i + 7j + k is

Question

Question

This question was previously asked in

ISRO URSC Technical Assistant Mechanical 13 Nov 2016 Official Paper

Answer 1

Concept:

If a triangle is formed by three vectors, then the sum of the vectors should be zero.

AB + BC + CA = 0

Cross product of the vectors:

For two vectors and the cross, the product is given by:

The magnitude of the cross product is:

Area of a triangle:

If the vectors form adjacent sides of the triangle then the area of the triangle is given by:

Calculation:

Given:

Let, AB = 3i + 4j and CA = 5i +7j + k

If a triangle is formed by three vectors, then the sum of the vectors should be zero.

AB + BC + CA = 0 ⇒ 3i + 4j + BC + 5i +7j + k = 0

BC = - 8i - 11j - k

Let the adjacent vectors be AB (a), AC (b) , and .

First, we will calculate the cross product as follow:

Therefore, the magnitude of the cross product is:

Using the formula for the area of the triangle, the area is given by: