Find vector v such that the area of the parallelogram spanned by u and v is 10. u = < -1, 4, -2 >
W warwick Full Member Joined Jan 27, 2006 Messages 311 Feb 13, 2008 #1 Find vector v such that the area of the parallelogram spanned by u and v is 10. u = < -1, 4, -2 >
pka Elite Member Joined Jan 29, 2005 Messages 11,995 Feb 14, 2008 #2 If v=⟨x,1,1⟩\displaystyle v = \left\langle {x,1,1} \right\ranglev=⟨x,1,1⟩ then we need to find x such that ∥v×u∥=10\displaystyle \left\|{v\times u}\right\|=10∥v×u∥=10
If v=⟨x,1,1⟩\displaystyle v = \left\langle {x,1,1} \right\ranglev=⟨x,1,1⟩ then we need to find x such that ∥v×u∥=10\displaystyle \left\|{v\times u}\right\|=10∥v×u∥=10
W warwick Full Member Joined Jan 27, 2006 Messages 311 Feb 14, 2008 #3 pka said: If v=⟨x,1,1⟩\displaystyle v = \left\langle {x,1,1} \right\ranglev=⟨x,1,1⟩ then we need to find x such that ∥v×u∥=10\displaystyle \left\|{v\times u}\right\|=10∥v×u∥=10 Click to expand... So, basically, we can choose an easy vector v to work with then solve for the unknown with the given information to complete the unknown vector.
pka said: If v=⟨x,1,1⟩\displaystyle v = \left\langle {x,1,1} \right\ranglev=⟨x,1,1⟩ then we need to find x such that ∥v×u∥=10\displaystyle \left\|{v\times u}\right\|=10∥v×u∥=10 Click to expand... So, basically, we can choose an easy vector v to work with then solve for the unknown with the given information to complete the unknown vector.
