How do you find the component form of $v = u + 2 w$ $v=u+2w$ given $u = 2 i - j, w = i + 2 j$ $u=2i-j, w=i+2j$ ?

Question

2245 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-27T15:36:05

$v = 4 i + 3 j$ $v = color(blue)(4i+3j)$

If $v = u + 2 i - j$ $v=u+2i-j$ and $w = i + 2 j$ $w=i+2j$

You just substitute these into $u + 2 w$ $u + 2w$

$v = 2 i - j + 2 (i + 2 j) = 2 i - j + 2 i + 4 j$ $v = 2i-j + 2(i +2j)= 2i -j+2i+4j$

Collect like terms:

$v = 2 i - j + 2 i + 4 j = 4 i + 3 j$ $v = 2i -j+2i+4j= 4i+3j$

So:

$v = 4 i + 3 j$ $v = color(blue)(4i+3j)$

How do you find the component form of v=u+2wv=u+2wv=u+2w given u=2i-j, w=i+2ju=2i−j,w=i+2ju=2i-j, w=i+2j?