UPSC NDA Math Model Paper 3

Consider, A=(λ

^

i

+

^

j

−

^

k

)=(λ,1,−1)
and B=(3

^

i

−2

^

j

+4

^

k

)=(3,−2,4)
and C=(2

^

i

−11

^

j

−7

^

k

)=(2,−11,−7)
Given A×B=C
We know that, Let A=(u1,u2,u3) and B=(v1,v2,v3) be any two vectors then its cross product is
A×B:(u1,u2,u3)×(v1,v2,v3) =(u2v3−u3v2,u3v1−u1v3,u1v2−u2v1)
Consider A×B=C
A×B:(λ,1,−1)×(3,−2,4) =((1)(4)−(−1)(−2),(−1)(3) −(λ)(4),(λ)(−2)−(1)(3))=(2,−11,−7)
⇒(2,−3−4λ,−2λ−3) =(2,−11,−7)
Vectors are equal. Their corresponding elements are equal.
⇒−2λ−3=−7
⇒2λ+3=7
⇒λ=2