Question

The angle between the planes `vec"r".(2hat"i" - 3hat"j" + hat"k")` = 1 and `vec"r"(hat"i" - hat"j")` = 4 is `cos^-1 ((-5)/sqrt(58))`.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

The given planes are `vec"r".(2hat"i" - 3hat"j" + hat"k")` and `vec"r".(hat"i" - hat"j")` = 4

Here, `vec"b"_1 = 2hat"i" - 3hat"j" + hat"k"` and `vec"b"_2 = (hat"i" - hat"j")`

So, `cos theta = (vec"b"_1 . vec"n"_2)/(|vec"b"_1||vec"n"_2|)`

⇒ `cos theta = ((2hat"i" - 3hat"j" + hat"k").(hat"i" - hat"j"))/(sqrt(4 + 9 + 1)*sqrt(1 + 1)`

= `(2 + 3)/(sqrt(14)*sqrt(2)`

= `5/sqrt(28)`

∴ `theta = cos^-1 (5/sqrt(28))` which is false.