Question

Area of a parallelogram, whose diagonals are
3i^+j^-2k^ and î - 3j^+ 4k^ will be :​

Answer 1

ᴠ = 3ɪ + ᴊ - 2ᴋ = ᴠ1 ɪ + ᴠ2 ᴊ + ᴠ3 ᴋ 

ᴡ = ɪ - 3ᴊ + 4ᴋ = ᴡ1 ɪ + ᴡ2 ᴊ + ᴡ3 ᴋ 

ᴠ x ᴡ = (ᴠ2 ᴡ3 - ᴠ3 ᴡ2) ɪ + (ᴠ3 ᴡ1 - ᴠ1 ᴡ3) ᴊ + (ᴠ1 ᴡ2 - ᴠ2 ᴡ1) ᴋ 

ᴠ x ᴡ = (1 * 4 - (-2) * (-3)) ɪ + ((-2) * 1 - 3 * 4) ᴊ + (3 * (-3) - 1 * 1) ᴋ 

ᴠ x ᴡ = (4 - 6) ɪ + (-2 - 12) ᴊ + (-9 - 1) ᴋ 

ᴠ x ᴡ = -2 ɪ - 14 ᴊ - 10 ᴋ 

Area = || ᴠ x ᴡ || = √ ( (-2) ² + (-14) ² + (-10) ² ) = 17.32