Question

vector u has initial point at (6,8) and terminal point at (3,-2). vector v has initial point at (-4,-3) and terminal point at (1,-7). what is u - v in component form? (8,-8) (2,-6) (8,6) (12,16)

Explanation:

Step1: Find component form of vector \(u\)

If a vector has initial point \((x_1,y_1)\) and terminal point \((x_2,y_2)\), its component form is \(\langle x_2 - x_1,y_2 - y_1
angle\).
For vector \(u\) with initial point \((6,8)\) and terminal point \((3,- 2)\), we have \(u=\langle3 - 6,-2 - 8
angle=\langle-3,-10
angle\)

Step2: Find component form of vector \(v\)

For vector \(v\) with initial point \((-4,-3)\) and terminal point \((1,-7)\), we have \(v=\langle1-(-4),-7 - (-3)
angle=\langle5,-4
angle\)

Step3: Calculate \(u - v\)

If \(u=\langle a,b
angle\) and \(v=\langle c,d
angle\), then \(u - v=\langle a - c,b - d
angle\).
Here \(a=-3,b = - 10,c = 5,d=-4\), so \(u - v=\langle-3-5,-10-(-4)
angle=\langle-8,-6
angle\)

Answer:

\(\langle - 8,-6
angle\)