Question

Solve the following problem.

Given `vec"v"_1 = 5hat"i" + 2hat"j" and vec"v"_2 = "a"hat"i" - 6hat"j"` are perpendicular to each other, determine the value of a.

Answer 1

As `vec"v"_1 and vec"v"_2` are perpendicular to each other, θ = 90°

`vec"v"_1*vec"v"_2 = 0`

∴ `(5hat"i" + 2hat"j")*("a"hat"i" - 6hat"j")` = 0

∴ `(5hat"i"*"a"hat"i") + (2hat"j"*6hat"j") = 0   ....(because hat"i"*hat"j" = hat"j"*hat"i" =0)`

∴ 5a + (-12) = 0     ...`(because hat"i"*hat"i" = hat"j"*hat"j" = 1)`

∴ 5a = 12

∴ a = `12/5`

Value of a is `12/5`.