the following vectors span a parallelepiped P: U=c V= W=, c cannot = 0 Find the value of c such that Vol(P)=8 and the angle (theta) between U and V is acute (i.e. 0

Question

the following vectors span a parallelepiped P: U=c<1,1,1> V=<1,0,2> W=<-1,-1,3>, c cannot = 0 Find the value of c such that Vol(P)=8 and the angle (theta) between U and V is acute (i.e. 0< theta< (pie/2) ) @ganeshie8

anonymous · Answer

i found that c=2 well |c|=2
and ik that to find theta it's 
(vector U * vectorV)/(||vector U|| ||vector V|| = Cos (theta)

i got upto
Cos(theta)= (3c)/(|c|(sqr(15))
but...

anonymous · Answer

to be acute c>0

anonymous · Answer

so that's it? does c>0 validate
c=2?

ganeshie8 · Answer

scalar triple product of given 3 vectors gives you the volume

anonymous · Answer

but what good does that equation i found equal to cos(theta) do for finding if the angle is acute?

ganeshie8 · Answer

Looks good ! the angle is acute when $c$ is positive as $\cos$ is positive in first quadrant

ganeshie8 · Answer

both c=2 and c=-2 give you the same volume 8
the question just wants you pick c=2, thats all

anonymous · Answer

Thank you for verifying!

ganeshie8 · Answer

yw!