Compute \((3,-2)+(0,0)\).

Find the additive inverse of \((4,-7)\).

A particle moves \(5\) m east and then \(5\) m west. Find the resultant displacement.

For \(\mathbf a=(1,2,3)\), calculate \(\mathbf a-\mathbf a\).

Find \(\mathbf x\) if \(\mathbf x+(2,-5)=(2,-5)\).

Forces \((6,-1)\) N and \((-6,1)\) N act together. Find the resultant.

What is the magnitude of \((0,0,0)\)?

Compute \(-3(0,0,0)\).

Find \(k\) if \(k(2,-1)=(0,0)\).

Find \(\mathbf v\) if \(4\mathbf v=(0,0,0)\).

Show that displacements \((2,1)\), \((3,-4)\), and \((-5,3)\) form a closed route.

If \(\mathbf a=(7,-2,5)\), find \(\mathbf b\) such that \(\mathbf a+\mathbf b=\mathbf0\).

Can \((0,0)\) have a unique direction angle? Justify using magnitude.

Solve \((x+2,3-y)=(0,0)\).

A body is in equilibrium under \((3,4)\) N, \((-8,1)\) N, and \(\mathbf F\). Find \(\mathbf F\).

For \(\mathbf u=(a,2a-6)\), decide whether any \(a\) makes \(\mathbf u=\mathbf0\).

If \(\mathbf p=(2,-3,1)\) and \(\mathbf q=(-4,6,-2)\), find \(2\mathbf p+\mathbf q\).

A vector \(\mathbf v\) satisfies \(\mathbf v+\mathbf w=\mathbf w\) for every \(\mathbf w\in\mathbb R^2\). Determine \(\mathbf v\), and verify your answer using \(\mathbf w=(3,-4)\).

Show that \(\overrightarrow{AB}=(1,5)\), \(\overrightarrow{BC}=(-4,2)\), and \(\overrightarrow{CD}=(3,-7)\) imply \(D=A\), then find the missing displacement if the final leg were instead required to end at \(D=A+(2,-1)\).

Solve \(s(1,-2,4)+t(0,0,0)=(0,0,0)\), and explain why this differs from solving \(s(1,-2,4)+t(2,-4,8)=\mathbf0\).