Question

For what value of 'a' the vector 2i-3j+4k and ai+6j-8k are collinear

Answer 1

Answer:

The 2 vectors will be collinear if they are parallel to each other. They will be parallel to each other if the second vector is a scalar multiple of the first one. Thus, a=-4.

Answer 2

The value of a is -4.

Step-by-step explanation:

If vectors u and v are collinear, then

$u=\lambda v$

where, λ is some scalar.

In other words, the corresponding components of collinear vectors are proportional.

If two vectors are $u=a_1i+b_1j+c_1k$ and $v=a_2i+b_2j+c_2k$, then

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

Given vectors are 2i-3j+4k and ai+6j-8k.

$\dfrac{2}{a}=\dfrac{-3}{6}=\dfrac{4}{-8}$

$\dfrac{2}{a}=\dfrac{-1}{2}$

On cross multiplication we get

$4=-a$

$-4=a$

Therefore, the value of a is -4.

#Learn more

For what value of ‘a’ the vectors 2i-3j+4k and ai+6j-8k are collinear?

https://brainly.in/question/5219577