Question

9. Find the area of the triangle formed by points O, A
and B such that OA = i + 2j + 3 kand
OB =-3 î - 2j+ k
​

Answer 1

Given:

OA = i + 2j + 3 k and  OB = -3 î - 2j+ k

To find:

Find the area of the triangle formed by points O, A  and B such that OA = i + 2j + 3 k and   OB =-3 î - 2j+ k

Solution:

From given, we have,

OA = i + 2j + 3 k and   OB =-3 î - 2j+ k

Area of triangle OAB = 1/2 × (OA × OB)

where OA × OB represents the cross product of vectors.

So, we have,

Area of Δ OAB = 1/2 × [ (1i + 2j + 3k) × (-3i - 2j + k) ]

= 1/2 × [ (2 × 1 - 3(-2)    (3(-3) - 1 × 1)     (1 (-2) - 2(-3)) ]

= 1/2 × (8   -10    4)

= 1/2 × √(8² + (-10)² + 4²)

= 1/2 × √(64 + 100 + 16)

= 1/2 × √180

= 1/2 × 6√5

= 3√5

​∴ The area of the triangle formed by points O, A  and B is 3√5 sq. units

Answer 2

1. Explanation:

This is done by using cross product and then do find magnitude by doing square and u can get the results