(Solved): (1 point) Resolve the following vectors into components: (a) The vector \( \vec{v} \) in 2-space o ...

(1 point) Resolve the following vectors into components: (a) The vector \( \vec{v} \) in 2-space of length 7 pointing up at an angle of \( \pi / 4 \) measured from the positive \( x \)-axis. \[ \vec{v}=\quad \vec{i}+\quad \vec{j} \] (b) The vector \( \vec{w} \) in 3-space of length 5 lying in the \( x z \)-plane pointing upward at an angle of \( 3 \pi / 4 \) measured from the positive \( x \)-axis. \[ \vec{v}= \] \[ \vec{i}+\quad \vec{j}+ \] \( \vec{k} \)