Question

The vectors from origin to the points A and B are A−→=3i^−6j^+2k^ and B−→=2i^+j^−2k^ respectively. The area of the triangle OAB be

Answer 1

Answer:

6.8

Explanation:

The vectors from origin to the points A and B are A−→=3i^−6j^+2k^ and B−→=2i^+j^−2k^ respectively. The area of the triangle OAB be

Origin = (0 , 0 , 0)

A   = ( 3 , 6 , 2)

B = (2 ,  1 , 2)

OA = √(3² + 6² + 2²) = √(9 + 36 + 4) = √49 = 7

OB = √(2² + 1² + 2²) = √(4 + 1 + 4) = √9 = 3

AB = √((3-2)² + (6-1)² + (2-2)²) = √(1 + 25) = √26

s = (7 + 3 + √26)/2 = 5 + √26/2

Area using hero formula

Area = √ (5 + √26/2) (-2 +  √26/2)(2 +  √26/2) (5 + √26/2)

=> Area = √ ( 25  - 26/4)( 26/4 - 4)

=> Area = √ ( 25  - 13/2)(13/2 - 4)

=> Area = √ ( 37/2)( 5/2)

=> Area = √185 /2

=> Area = 13.6 /2

=> Area = 6.8