How do you find a) u+v, b) u-v, c) 2u-3v given $u = i + j, v = 2 i - 3 j$ $u=i+j, v=2i-3j$ ?

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Answer 1 · 2017-12-18T10:16:47

See the explanation below

The vectors are

$\to u = ˆ i + ˆ j$ $vecu=hati+hatj$

$\to v = 2 ˆ i - 3 ˆ j$ $vecv=2hati-3hatj$

Therefore,

$(a)$ $(a)$

$\to u + \to u = ˆ i + ˆ j + 2 ˆ i - 3 ˆ j = 3 ˆ i - 2 ˆ i$ $vecu+vecu=hati+hatj+2hati-3hatj=3hati-2hati$

$(b)$ $(b)$

$\to u - \to u = ˆ i + ˆ j - 2 ˆ i + 3 ˆ j = - ˆ i + 4 ˆ i$ $vecu-vecu=hati+hatj-2hati+3hatj=-hati+4hati$

$(c)$ $(c)$

$2 \to u - 3 \to u = 2 (ˆ i + ˆ j) - 3 (2 ˆ i - 3 ˆ j)$ $2vecu-3vecu=2(hati+hatj)-3(2hati-3hatj)$

$= 2 ˆ i + 2 ˆ j - 6 ˆ i + 9 ˆ j$ $=2hati+2hatj-6hati+9hatj$

$= - 4 ˆ i + 11 ˆ j$ $=-4hati+11hatj$

How do you find a) u+v, b) u-v, c) 2u-3v given u=i+j,v=2i−3ju=i+j, v=2i-3j?