Thread: A question in Multivariable Calculus

Question
(1/3sqrt(2) )*<1,1,4> is a unit vector pointing in a direction opposite to the vector <-3,-3,-12>.

The answer is TRUE

Can you show me the working step of this question? Thank you very much.

Originally Posted by Jenny20

Question
(1/3sqrt(2) )*<1,1,4> is a unit vector pointing in a direction opposite to the vector <-3,-3,-12>.

The answer is TRUE

Can you show me the working step of this question? Thank you very much.

There are a couple of ways. I think the simplest would be to find the unit vector in the direction of <-3, -3, -12> and show that it adds to to make 0.

So the magnitude of the vector <-3,-3,-12> is . Thus the unit vector in the direction of <-3, -3, -12> is
.

You can easily see if you add this vector to the unit vector that the sum is 0.

-Dan

Thank you very much for your detailed explaination.