Linear Algebra volume

[Leo79]

Hi, I'm having difficulties answering Question 3b - I am unsure of how to work back through the equation to solve d. I've attached my working so far.

Any help would be much appreciated,

Leo

 

[Romsek]

I can't really understand your workings but

[MATH]Q \times R = \{-d-50,20-d,14\}[/MATH]
[MATH]P\cdot (Q\times R) = 38-4d[/MATH]
Work until your numbers match that. Then it's trivial to solve for [MATH]d[/MATH]

 

[Dr.Peterson]

An alternative approach is to use the fact that \(a\cdot(b\times c)=b\cdot(c\times a)=c\cdot(a\times b)\), which is equivalent to the fact that the volume is unaffected by interchanging the sides. So you can use \(r\cdot(p\times q)\) to save a little work.

 

[Leo79]

I can't really understand your workings but

[MATH]Q \times R = \{-d-50,20-d,14\}[/MATH]
[MATH]P\cdot (Q\times R) = 38-4d[/MATH]
Work until your numbers match that. Then it's trivial to solve for [MATH]d[/MATH]

Hi Romsek, Thanks very much I've got to that point now. In negotiating the length of P • (Q x R) I've got 38+4d/6 = 10.

Is this correct and can I just solve for d from here?

 

[Leo79]

Hi Romsek, Thanks very much I've got to that point now. In negotiating the length of P • (Q x R) I've got 38+4d/6 = 10.

Is this correct and can I just solve for d from here?

Is this correct? - sorry if it's messy

 

[Romsek]

Hi Romsek, Thanks very much I've got to that point now. In negotiating the length of P • (Q x R) I've got 38+4d/6 = 10.

Is this correct and can I just solve for d from here?

no.

[MATH] \dfrac{38-4d}{6}=10[/MATH]
careful with signs.