Question

given ( u = langle 2,-8
angle ) and ( v = langle 8,-2
angle ), what is ( u cdot v )?
-68
-60
0
32

Explanation:

Step1: Recall the dot - product formula

For vectors \(u=(u_1,u_2)\) and \(v=(v_1,v_2)\), \(u\cdot v = u_1v_1+u_2v_2\).

Step2: Substitute the values

Here \(u_1 = 2\), \(u_2=-8\), \(v_1 = 8\), \(v_2=-2\). Then \(u\cdot v=(2\times8)+(-8\times(-2))\).

Step3: Calculate each product

\(2\times8 = 16\) and \(-8\times(-2)=16\).

Step4: Sum the products

\(u\cdot v=16 + 16=32\).

Answer:

D. 32