Question

Determine m so that u and v are perpendicular. u=(2m,m-1,m+1);v=(m-1,m,m-1)

Answer 1

for \(u\) and \(v\) to be perpendicular solve
\[\large u\cdot v=0 \]

Answer 2

I did and i got 0=4m^2 - 3m - 1 , but it doesnt match up to the answer which is m=1 or -1/4

Answer 3

let's see
\[\large 0=u\cdot v=(2m,m-1,m+1)\cdot(m-1,m,m-1) \]
\[\large 0=2m(m-1)+(m-1)m+(m+1)(m-1) \]
\[\large 0=2m^2-2m+m^2-m+m^2-1 \]
\[\large 0=4m^2-3m-1 \]
\[\large 0=(m-1)(4m+1) \]
from this m=1 or m=-1/4

Answer 4

i got the same

Answer 5

Ohh i get it now, thanks

Answer 6

u r welcome