The cross product is a×b=(17, −22, −8), whose magnitude is√837≈28.93. Triangle area is half that, 14.46. Normalising gives approximately(0.588, −0.760, −0.277), matching C. The unnormalised cross product is not a unit vector.
More Vector Calculus questions
GATE 2023 MN Q14– Given A=3 i+2 j and B= i+ j, find the magnitude of the projection of A along B.
GATE 2022 MN Q12– A velocity field is v=x i+y j+p(z) k, with p(0)=0. If its divergence is zero, find p(z).
GATE 2022 MN Q14– For the vectors x and y shown, which expression is the vector projection of x onto nonzero…
GATE 2021 MN Q18– For the coplanar vectors shown, let c=( a+ b)( a- b). Its magnitude equals which quantity?
GATE 2026 MN Q12– Find the divergence of F=x2y i+y3x j at (3,2).
GATE 2025 MN Q56– Find the directional derivative of f=4x2+8y2+9z2 at(3,4,5),along 2 i-3 j+4 k,to one…