Question

if vector A=2i^-2j^+k^ and vector B = 4i^+2j^-4k^. Show that Aand B vector are perpendicular to each other​

Answer 1

Answer:

Given that, vector A = 2î - 2j + k and vector B = 4î + 2j - 4k.

|A| = √(2² + 2² + 1²) = √(4 + 4 + 1) = √9 = 3.

|B| = √(4² + 2² - 4²) = √2² = 2.

If these two vectors are perpendicular to each other, then the angle between these two vectors will be 90°.

We know that, cos ∅= A•B/|A||B|

Therefore, cos ∅ = A•B/|A||B|

⇒ cos ∅ = (2î - 2j + k)(4î + 2j - 4k)/3•2

⇒ cos ∅ = (8 - 4 - 4)/6

⇒ cos ∅ = (4 - 4)/6

⇒ cos ∅ = 0/6

⇒ cos ∅ = 0

We know that, cos ∅ = 0, when ∅ = 90°.

Hence, Proved.