Question

Find the area of parallelogram formed by vectors a=3i+2j,b=-3i+7j

Answer 1

Find the area of parallelogram formed by vectors a=3i+2j,b=-3i+7j

answer : 27 sq unit

explanation : you should remember that area of any two dimensional or three dimensional shape is a vector quantity. it is always perpendicular to its plane.

so, area of parallelogram formed by two adjacent sides a and b = cross product of a and b.

or, A = |a × b|

       = |(3i + 2j) × (-3i + 7j)|

      = |3i × (-3i) + 3i × 7j + 2j × (-3i) + 2j × 7j|

[ we know,  i × i = 0 , i × j = k , j × k = i, k × i = j , j × j = 0, j × i = - k]

     = |0 + 21 k -(-6)k + 0|   = |27k| = 27 sq unit

hence area of parallelogram is 27 sq unit.

Answer 2

Answer:

The area of the parallelogram is 27 square units