# Thread: A question in Multivariable Calculus

1. ## 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.

2. 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 $\frac{1}{3\sqrt{2}}<1, 1, 4>$ to make 0.

So the magnitude of the vector <-3,-3,-12> is $\sqrt{162} = 9\sqrt{2}$. Thus the unit vector in the direction of <-3, -3, -12> is
$\frac{<-3, -3, -12>}{9\sqrt{2}} = -\frac{1}{3\sqrt{2}}<1, 1, 4>$.

You can easily see if you add this vector to the unit vector $\frac{1}{3\sqrt{2}}<1, 1, 4>$ that the sum is 0.

-Dan

3. Thank you very much for your detailed explaination.