Answer to Question #307572 in Analytic Geometry for Cee

Question

Two nonzero vectors a and b are called perpendicular or orthogonal if the angle between them is Blank 1. Fill in the blank, read surrounding text.

and a⋅ b= Blank 2. Fill in the blank, read surrounding text.

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Answer 1

Answers

1)

• They are called perpendicular to each other if the angle between them is 90 degrees.

2)

1. The dot product hence becomes 0 (a.b = 0) as per its definition.

$\qquad\qquad \begin{aligned} \small \underline{a}.\underline{b}&=\small ab\cos\theta\\ &=\small ab\cos 90^0\\ &=\small ab\times0\\ \small \underline{a}.\underline{b}&=\small 0 \end{aligned}$