Question

The value of λ for which the vectors $2i-3j+4k$ and $-4i+λj-8k$ are collinear is

• A. $0$
• B. $1$
• C. $3$
• D. $6$
• E. $4$

Answer 1

Answer: (D)

$6$

Answer 2

Given that :
The two vectors are
$2i-3j+4k$ and $-4i+λj-8k$ (are collinear )
So we know that the cross product of two collinear vector is zero.
hence,the same can be represented as
$⇒i((-3×-8)-4λ)-j((2×-8)-(-4×4))+k((2λ)-(-3×-4))=0$
$⇒i(24-4λ)-j(0)+k(2λ-12)=0$
So Take , $24-4λ=0$ and $2λ-12=0$
$⇒λ=6$ $⇒λ=6$
Therefore for the given collinear vectors the value of $λ$ is $6$.
So, the correct option is (C) : 6.