Compute \((2,3)+(4,-1)\).

A walker moves \(5\) m east then \(2\) m east. Find the resultant displacement.

Compute \(3\mathbf i-2\mathbf j+(-5\mathbf i+7\mathbf j)\).

A boat travels \(4\) km north then \(3\) km east. Write the resultant vector and magnitude.

Find \((1,-4,2)+(6,0,-5)\).

Find \(\overrightarrow{AC}\) if \(\overrightarrow{AB}=(3,4)\) and \(\overrightarrow{BC}=(3,-5)\).

Three forces are \((2,1)\) N, \((-5,3)\) N, and \((4,-6)\) N. Find the resultant.

A drone moves \((1,2,0)\) m, then \((0,-3,4)\) m. Find final displacement from the start.

Find \(\mathbf a+\mathbf b\) and its magnitude for \(\mathbf a=(6,2)\), \(\mathbf b=(-1,10)\).

Find \(\mathbf x\) if \(\mathbf x+(2,-7)=(5,1)\).

A hiker walks \(6\) km east, \(2\) km south, then \(1\) km west. Find resultant vector and magnitude.

Compute \(\mathbf p+\mathbf q+\mathbf r\) for \(\mathbf p=(2,-1,3)\), \(\mathbf q=(-4,5,0)\), \(\mathbf r=(1,1,-6)\).

Given \(\overrightarrow{AB}=(4,-2)\) and \(\overrightarrow{AC}=(1,5)\), find \(\overrightarrow{BC}\).

Two tugs pull with forces \(8\) N east and \(6\) N north. Find resultant magnitude and direction north of east.

A particle moves from \(A=(1,-2,3)\) to \(B=(4,0,-1)\), then to \(C=(-2,5,2)\). Find the resultant displacement and the total path length travelled.

Three coplanar forces keep a joint in equilibrium. Two forces are \((3,-8)\) N and \((-1,5)\) N. Find the third force and its magnitude.

A drone starts at \((2,1,5)\), makes displacements \((-4,3,2)\) and \((1,-6,-7)\), then must end at \((0,0,4)\). Find the final correction displacement.

A robot starts at \((1,2)\), moves by \(2\mathbf i-\mathbf j\), then by \(-3\mathbf i+4\mathbf j\), then by \(\mathbf i-6\mathbf j\). Find its final position and the single displacement that would return it to the start.

Air velocity is \((90,0)\) km h\(^{-1}\) and wind velocity is \((-20,15)\) km h\(^{-1}\). Find ground velocity and speed.

Four displacement vectors form a closed path: \((2,5)\), \((-1,3)\), \((4,-6)\), and \(\mathbf d\). Find \(\mathbf d\).