Question

Find 'a' if vector A = 3i^ -2j^ +4k^ and vector B =ai^+2j^-k^ are prependicular to one another

Answer 1

Hi,

It is given that vector A and vector B are perpendicular to each other.
Hence dot product will be zero.
Please find the attached solution.

Thanks,
Khushboo

Answer 2

concepts :- when two A and B are perpendicular upon each other ,then dot product of A and B equals zero.
e.g., A.B = 0
If A = a₁i + a₂j + a₃k and B = b₁i + b₂j + b₃k
Then, A.B = a₁b₁ + a₂b₂ + a₃.b₃

Now come to the question,
A = 3i - 2j + 4k and B = ai + 2j - k
A.B = 3 × a + -2 × 2 + 4 × -1 = 0
⇒3a - 4 - 4 = 0
⇒ a = 8/3

Hence, a = 8/3