Question

Another precalc vector problem... Please help?

If v=(1,2), w=(-1,2), and u=(5,12), for what scalar k will the vector kv+w be perpendicular to u?

Answer 1

@ganeshie8 maybe you could help me with this one too? :)

Answer 2

start by finding the vector : kv+w

Answer 3

\(\large k\vec{v} + \vec{w} = k<1, 2> + <-1, 2>\)

\(\large ~~~~~~~~~~= <k, 2k> + <-1, 2>\)

\(\large ~~~~~~~~~~= <k-1, 2k+2>\)

Answer 4

fine ?

Answer 5

next use this :
two vectors are perpendicular
=>
dot product = 0

Answer 6

take the dot product : (kv+w) . (u)
and set it equal to 0

Answer 7

Oh I got!
5k - 5 + 24k +24 = 0
29k + 19 = 0
29k = -19
k = -19/29

So it's -19/29, which is the answer my book says. Wasn't nearly as hard as it seemed! Thanks again.