CBSE Class 12 Sample Paper for 2019 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 10 (OR 1 st question)

Find the area of the parallelogram whose diagonals are represented by the vectors a = 2i  – 3j  + 4k and b = 2i – j + 2k

Transcript

Question 10 (OR 1st question) Find the area of the parallelogram whose diagonals are represented by the vectors š ā = 2š Ģ ā 3š Ģ + 4š Ģ and š ā = 2š Ģ ā š Ģ + 2š Ģ Area of parallelogram with diagonals Area = 1/2 |(š_1 ) āĆ(š_2 ) ā | Given Diagonals of a parallelogram as š ā = 2š Ģ ā 3š Ģ + 4š Ģ and š ā = 2š Ģ ā š Ģ + 2š Ģ Area of the parallelogram = 1/2 |š āĆš ā | Finding š ā Ć š ā š ā Ć š ā = |ā 8(š Ģ&š Ģ&š Ģ@2&ā3&4@2&ā1&2)| = š Ģ ((ā3) Ć 2 ā (-1) Ć 4) ā š Ģ (2 Ć 2 ā 2 Ć 4) + š Ģ (2 Ć (-1) ā 2 Ć (-3)) = š Ģ (-6 + 4) ā š Ģ (4 ā 8) + š Ģ (ā2 + 6) = š Ģ (ā2) - š Ģ (ā4) + š Ģ (4) = ā2š Ģ + 4š Ģ + 4š Ģ So, Magnitude of š ā Ć š ā = ā((ā2)2+(4)2+(4)2) |š ā" Ć " š ā | = ā(4+16+16) |š ā" Ć " š ā |= ā36 |š ā" Ć " š ā |= 6 Thus, Area of the parallelogram = 1/2 |š āĆš ā | = 1/2 Ć 6 = 3 square units