Question

current attempt in progress
the two vectors shown in the figure lie in an xy plane. what are the signs of the x and y compo
(a) \\(\vec{d}_1 + \vec{d}_2\\)
(b) \\(\vec{d}_1 - \vec{d}_2\\)
(c) \\(\vec{d}_2 - \vec{d}_1\\)

Explanation:

Step1: Analyze vector components

For $\vec{d_1}$: $x$-component negative, $y$-component negative.
For $\vec{d_2}$: $x$-component negative, $y$-component positive.

Step2: Solve $\vec{d_1} + \vec{d_2}$

Add corresponding components:
$x$-component: $(-) + (-) = -$
$y$-component: $(-) + (+)$: The magnitude of $\vec{d_2}$'s $y$-component is larger, so $+$
Result: $x$-negative, $y$-positive

Step3: Solve $\vec{d_1} - \vec{d_2}$

Rewrite as $\vec{d_1} + (-\vec{d_2})$, $-\vec{d_2}$ has $x$-positive, $y$-negative components:
$x$-component: $(-) + (+)$: The magnitude of $\vec{d_1}$'s $x$-component is larger, so $-$
$y$-component: $(-) + (-) = -$
Result: $x$-negative, $y$-negative

Step4: Solve $\vec{d_2} - \vec{d_1}$

Rewrite as $\vec{d_2} + (-\vec{d_1})$, $-\vec{d_1}$ has $x$-positive, $y$-positive components:
$x$-component: $(-) + (+)$: The magnitude of $-\vec{d_1}$'s $x$-component is larger, so $+$
$y$-component: $(+) + (+) = +$
Result: $x$-positive, $y$-positive

Answer:

(a) $x$-component: negative, $y$-component: positive
(b) $x$-component: negative, $y$-component: negative
(c) $x$-component: positive, $y$-component: positive