Find the Coordinates of Point B using Cross Product

[Melawrghk]

Homework Statement

Point A is at (0,3,0), D(0, 0, 3), C(4, 0, 0) and B(x,y,z). The bar AB is 7.09 m long and is perpendicular to the bars AC and AD. Use the cross product to determine the coordinates of x, y, and z.

Homework Equations

The cross product matrix thing...

The Attempt at a Solution

I found the eqations for AC and AD. I know that if I find their cross product, I will get AB, which is essentially what I'm looking for.
AC = 4i-3j+0k
AD = 0j-3j+3k

When I found the cross product of them in this form, I got it wrong. Also, I'm not sure which order to put them in, which one goes first, AC or AD? I now am attempting to convert them to unit vectors and do the cross product with those, but again, I'm not sure about the order. Help?

Thanks

 

[LowlyPion]

Homework Statement

Point A is at (0,3,0), D(0, 0, 3), C(4, 0, 0) and B(x,y,z). The bar AB is 7.09 m long and is perpendicular to the bars AC and AD. Use the cross product to determine the coordinates of x, y, and z.

Homework Equations

The cross product matrix thing...

The Attempt at a Solution

I found the eqations for AC and AD. I know that if I find their cross product, I will get AB, which is essentially what I'm looking for.
AC = 4i-3j+0k
AD = 0j-3j+3k

When I found the cross product of them in this form, I got it wrong. Also, I'm not sure which order to put them in, which one goes first, AC or AD? I now am attempting to convert them to unit vectors and do the cross product with those, but again, I'm not sure about the order. Help?

Thanks

I don't think it's going to make a difference as to whether you do AC X AD or AD X AC. Won't the sign of the Resulting vector still be along the direction of AB but the sign of the coefficients of the components i,j,k will be reversed?

When I did the X-product of AD X AC I got in i,j,k an AB direction Resultant of (9,12,12), and for the AC X AD product got (-9,-12,-12), but it nominally points in the opposite direction. Knowing the direction of the resultant you should be able to solve for the intersection of B(x,y,z) no?

 

[HallsofIvy]

You are not asked for the cross product itself. The cross product will give you a vector perpendicular to both AC and AD but NOT the point (x,y,z) you want. To find a vector perpendicular to both AC and AD AND with length 7.09, divide the cross product by its length (to get a vector with length 1) and then multiply that unit vector by 7.09. There are actually two possible answers, one with coordinates the negative of the other.