Consider the following vectors. u = (-7, 15), v = (-(5)/(7),...

Consider the following vectors. u = (-7, 15), v = \left(-\frac{5}{7}, \frac{1}{3}\right) Find the dot product of the two vectors. \mathbf{u} \cdot \mathbf{v} = 0 Find a scalar value $c$ such that $\mathbf{u} = c\mathbf{v}$. (If such a value does not exist, enter DNE.) c = DNE Determine whether \mathbf{u} and \mathbf{v} are orthogonal, parallel, or neither. $\circ$ orthogonal $\circ$ parallel $\circ$ neither

Transcript

00:03 All right.

00:04 Here, number 18, we're given two vectors, v and w, and we're given them in terms of the standard unit vectors i and j.

00:13 But obviously, you can put them in component form quite easily.

00:18 I is the standard horizontal, or the horizontal standard unit vector, 1 -0.

00:22 And negative 3j would be in component form 0 -9 -3.

00:28 So i like to work with them in component form.

00:31 So i'll do that first.

00:32 So we want to be.

00:33 To find their dot product and we want to find the angle between them using the formula there you see in the upper right hand corner and then we want to determine if the vectors are parallel orthogonal or neither and that you can do at any point in time um along the way in fact we will know that answer immediately upon doing part a finding the dot product if you're observant you might recognize that the two vectors, one of them is vertical and the other one is horizontal.

01:10 If one's going straight one way and the other one's going vertically, then it has to be, those have to be perpendicular or orthogonal.

01:21 And that means the angle between them is going to be 90 degrees.

01:24 So we can answer all the questions with actually out doing any work if you're, you know, observant and you know your properties and such.

01:32 But we'll go through them anyway.

01:36 So for part b, or from part a, sorry, we're going to do the dot product.

01:40 So that's going to be 1 times 0 plus 0 times negative 3, which of course is 0 plus 0, which is 0.

01:51 Well, what does that tell us? that tells us that the vectors are orthogonal.

01:58 Perpendicular vectors, they're going to have a dot product of 0.

02:01 That also basically tells us part b because if the dot product is zero and they're orthogonal, that means the angle formed between them has to be a right angle.

02:11 It has to be 90 degrees...

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