Question

Please give me right answer. I will gave brainlist ​

Answer 1

diagonals of parallelogram are ;

d1 = 5i - 4j + 3k

d2 = 3i + 2j - k

we know, area of parallelogram in terms of diagonals is given by,

= 1/2 d1 * d2 * sinα

where d1 and d2 are the magnitude of diagonals of parallelogram and α is angle between them.

so, first find d1 and d2 ,

d1 = √{5² + (-4)² + 3²} = √50

d2 = √{3² + 2² + (-1)²} = √14

and angle between them, α = cos^-1 (d1 * d2)/ mod d1 * mod d2

= cos^-1{(5i -4j + 3k).(3i + 2j - k)}/√50.√14

= cos^-1{(15 - 8 - 3)/10√7}

= cos^-1(2/5√7)

so, sinα = sin(cos^-1(2/5√7)) = √171/5√7

so, area of parallelogram = 1/2 × √50 × √14 × √171/5√7

= 1/2 × 5√2 × (√7 × √2) × √171/5√7

= 1/2 × 2 × √171

= √171 sq unit .

= 13.4 units

Hope it Helps !!!!

Answer 2

The answer is 1st option that is 13.4units
Hope it helps you