Dot Product

[elleocin]

If the vectors a= (2,3,4) and b= (10,y,z) are perpendicular, how must y and z be related?

I came up with the equation 20 + 3y + 4z... problem is I don't know what to do with it.

The answer at the back says y= -4/3z - -20/3. I tried subbing 0 for each variable in the eqn but it didn't come out right

I feel like I'm making this more complicated than it really is. Anyways, help would be appreciated!!

 

[pka]

If the vectors a= (2,3,4) and b= (10,y,z) are perpendicular, how must y and z be related?

I came up with the equation 20 + 3y + 4z... problem is I don't know what to do with it.

The answer at the back says y= -4/3z and z= -20/3. I tried subbing 0 for each variable in the eqn but it didn't come out right

To be perpendicular the dot product must be zero.

So \(\displaystyle 20+3y+4z=0\).

 

[elleocin]

**EDIT: the answer is y= -4/3z - -20/3. Sorry for the confusion!

I know that the equation equals zero, but how do you get the values for y?

 

[pka]

**EDIT: the answer is y= -4/3z - -20/3. Sorry for the confusion!

I know that the equation equals zero, but how do you get the values for y?

Well I do not agree with that answer. There infinitely many valid answers.

\(\displaystyle y=\dfrac{-20-4z}{3}\) works for any \(\displaystyle z\).

 

[Bob Brown MSEE]

In the original wording of the question, "how must y and z be related?", does not require a value for each.
It only requires an equation relating y and z (as pka has provided).

Yea, its done!