Answer to Question #96506 in Analytic Geometry for Olajide Olaitan

Question

Determine the value a so that A=2i+aj+k and B=4i-2j-2k are perpendicular

Answer 1

We need to find the value of "a", when two vectors are perpendicular.

We know a formula

If Two Line are represented bye vectors $\vec {A}$ = $a_1 \vec {i} + a_2 \vec {j} + a_3 \vec {k}$

$\vec {B} = b_1 \vec {i} + b_2 \vec {j} + b_3 \vec {k}$ are perpendicular

Then $\vec {A} . \vec {B} = 0$

It means $a_1 b_1 + a_2 b_2 + a_3 b_3 = 0$

The given lines are $\vec {A} = 2 \vec {i} + a \vec {j} + 1 \vec {k}$ and $\vec {B} = 4 \vec {i} - 2 \vec {j} - 2 \vec {k}$ are perpendicular.

So, 2(4) +a (-2) +1 (-2) = 0

2a = 6

a= 3.

Answer: a = 3