Compute \(3(2,-5)\).

Compute \(-2(4\mathbf i-\mathbf j)\).

A vector \(\mathbf v=(3,4)\) is doubled. Find \(2\mathbf v\) and its magnitude.

Find \(\frac12(8,-6,10)\).

A displacement \((5,0)\) m is multiplied by \(-1\). Interpret the result.

Find \(k\) if \(k(2,3)=(10,15)\).

Calculate \(-3(1,-2,4)+2(0,5,-1)\).

A force \(\mathbf F=(4,-3)\) N is increased by a factor of \(2.5\). Find the new vector.

Find the unit vector in the direction of \(\mathbf a=(6,8)\).

Find a vector parallel to \((2,-1,2)\) with magnitude \(9\) and the same direction.

Determine whether \((12,-8)\) is a scalar multiple of \((-3,2)\).

Find \(a\) and \(b\) if \(4(a,b)=(-12,20)\).

For \(\mathbf u=(1,2)\) and \(\mathbf v=(-3,4)\), compute \(5\mathbf u-2\mathbf v\).

A velocity \((9,12)\) m s\(^{-1}\) is scaled to one third of its magnitude in the opposite direction. Find it.

Find \(t\) such that \(t(4,-2)\) has magnitude \(10\).

Verify \(2(\mathbf a+\mathbf b)=2\mathbf a+2\mathbf b\) for \(\mathbf a=(1,-3)\), \(\mathbf b=(4,5)\).

Find \(k\) so that \(k(3,4)\) has \(y\)-component \(-12\), then give the vector.

A line uses direction vector \(\mathbf b=(2,-1,3)\). Give two non-zero scalar multiples for the same line direction, then explain which one reverses the parameter direction.

Solve \(3(2x,1-x)=(12,-3)\), then decide whether \((2x,1-x)\) points in the same direction as \((12,-3)\).

A vector \(\mathbf a=(2,-2,1)\) is multiplied successively by \(k\) and \(m\), giving \((-18,18,-9)\). Find \(km\), and describe the effect on direction and length.