Question

for ( u = langle 5, - 2
angle ) and ( v = langle - 1,5
angle ), find ( u cdot v ).
( u cdot v = )

Explanation:

Step1: Recall the dot - product formula

If \(\mathbf{u}=\langle u_1,u_2
angle\) and \(\mathbf{v}=\langle v_1,v_2
angle\), then \(\mathbf{u}\cdot\mathbf{v}=u_1v_1 + u_2v_2\).
Here \(u_1 = 5\), \(u_2=-2\), \(v_1=-1\), \(v_2 = 5\).

Step2: Substitute the values into the formula

\(\mathbf{u}\cdot\mathbf{v}=(5)\times(-1)+(-2)\times(5)\)

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LATEXBLOCK0
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Answer:

\(-15\)