Question

If O be the origin and if the coordinates of any two points Q₁ and Q₂ be (x₁, y₁) and (x₂, y₂) respectively, then OQ₁. OQ₂cos Q₁OQ₂ =

• A. x₁x₂ – y₁y₂
• B. x₁y₁ – x₂y₂
• C. x₁x₂ + y₁y₂
• D. x₁y₁ + x₂y₂

Answer 1

Answer: (C)

x₁x₂ + y₁y₂

Answer 2

cos (ŠQ₁OQ₂) = $\frac{(OQ_{1})^{2} + (OQ_{2})^{2}–(Q_{1}Q_{2})^{2}}{2OQ_{1}.OQ_{2}}$

Ž OQ₁.OQ₂ cos (ŠQ₁OQ₂) = (OQ₁)² + (OQ₂)² – (Q₁Q₂)²

Ž $\frac{x_{1}^{2} + y_{1}^{2} + x_{2}^{2} + y_{2}^{2}–\{(x_{1}–x_{2})^{2} + (y_{1} + y_{2})^{2}\}}{2}$

Ž (x₁x₂ + y₁y₂).

Or

Let $\overset{\rightarrow}{OQ_{1}}$ = x₁i + y₂j

$\overset{\rightarrow}{OQ_{2}}$ = x₂i + y₂j

cos (ŠQ₁OQ₂) = $\frac{\overset{\rightarrow}{OQ_{1}}.\overset{\rightarrow}{OQ_{2}}}{OQ_{1}.OQ_{2}}$

Ž OQ₁.OQ₂ = x₁x₂ + y₁y₂.