Given vectors $s = -i + 2j$, $t = 3i - j$, and $r = 2i + 5j$, find: (a) $s+t$ (b) $r-s$ (c) $2t+r$

1. Problem Description

Given vectors $s = -i + 2j$, $t = 3i - j$, and $r = 2i + 5j$, find:

(a) $s+t$

(b) $r-s$

(c) $2t+r$

2. Solution Steps

(a) To find $s+t$, we add the corresponding components of the vectors $s$ and $t$:

$s + t = (-i + 2j) + (3i - j) = (-1+3)i + (2-1)j = 2i + j$.

(b) To find $r-s$, we subtract the corresponding components of the vectors $s$ from $r$:

$r - s = (2i + 5j) - (-i + 2j) = (2 - (-1))i + (5-2)j = (2+1)i + 3j = 3i + 3j$.

(c) To find $2t+r$, we first multiply the vector $t$ by 2, then add the vector $r$:

$2t = 2(3i - j) = 6i - 2j$

Then we add $r$ to $2t$:

$2t + r = (6i - 2j) + (2i + 5j) = (6+2)i + (-2+5)j = 8i + 3j$.

3. Final Answer

(a) $s+t = 2i + j$

(b) $r-s = 3i + 3j$

(c) $2t+r = 8i + 3j$