Find the area of a triangle joining the points A(1,1,1), B(1,2,3), and C(2,3,1) as its vertices.

The above question is from the vectors chapter. 

Asked by sujaychandramouli | 24th May, 2022, 10:46: AM

Expert Answer:

Here comma space OA with rightwards arrow on top equals straight i plus straight j plus straight k comma space OB with rightwards arrow on top equals straight i plus 2 straight j plus 3 straight k comma space OC with rightwards arrow on top equals 2 straight i plus 3 straight j plus straight k
AB with rightwards arrow on top equals OB with rightwards arrow on top minus OA with rightwards arrow on top equals straight j plus 2 straight k comma space AC with rightwards arrow on top equals OC with rightwards arrow on top minus OA with rightwards arrow on top equals straight i plus 2 straight j
AB with rightwards arrow on top cross times AC with rightwards arrow on top equals open vertical bar table row straight i straight j straight k row 0 1 2 row 1 2 0 end table close vertical bar equals straight i left parenthesis negative 4 right parenthesis minus straight j left parenthesis negative 2 right parenthesis plus straight k left parenthesis negative 1 right parenthesis equals negative 4 straight i plus 2 straight j minus straight k
Area space of space triangle space ABC equals 1 half open vertical bar AB with rightwards arrow on top cross times AC with rightwards arrow on top close vertical bar equals 1 half square root of 16 plus 4 plus 1 end root equals fraction numerator square root of 21 over denominator 2 end fraction space sq. space units

Answered by Renu Varma | 27th May, 2022, 11:48: AM