Question

4. The diagonals of a parallelogram are represented by vectors P = 31-4
Then the area of the parallelogram is
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Answer 1

Explanation:

diagonals of parallelogram are ;

 = 5i - 4j + 3k

 = 3i + 2j - k

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

 = √{5² + (-4)² + 3²} = √50

 = √{3² + 2² + (-1)²} = √14

and angle between them, α = cos^-1

= 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 .