Question

If the line r = `(hat"i" - 2hat"j" + 3hat"k") + lambda(2hat"i" + hat"j" + 2hat"k")` is parallel to the plane `"r" * (3hat"i" - 2hat"j" + "m"hat"k")` = 10, then the value of m is ______.

Options

• - 2

• 3

• 2

• - 3

Answer 1

If the line r = `(hat"i" - 2hat"j" + 3hat"k") + lambda(2hat"i" + hat"j" + 2hat"k")` is parallel to the plane `"r" * (3hat"i" - 2hat"j" + "m"hat"k")` = 10, then the value of m is -2.

Explanation:

Given line, 

r = `(hat"i" - 2hat"j" + 3hat"k") + lambda(2hat"i" + hat"j" + 2hat"k")`

is parallel to plane `"r" * (3hat"i" - 2hat"j" + "m"hat"k")` = 0

We know that, if line r = `"a" + lambda"b"` is parallel to plane r·n = d

Then, b · n = 0

`therefore (2hat"i" + hat"j" + 2hat"k") * (3hat"i" - 2hat"j" + "m"hat"k")` = 0

6 - 2 + 2m = 0.

m = - 2