Show that the perpendicular distance of the point c- from the line joining a- and b- is - b-c-c-a-a-b- - b-a-

Area of || gm ABCD = Base × Height = ||AB||b HeightArea also equals to || AC×AB|| ||AB|| Height =||AC×AB || Height ( dist ...

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Applications of Cross Product

Show that the...

Question

Show that the perpendicular distance of the point $\to c$ from the line joining $\to a$ and $\to b$ is $\frac{∣ ∣ \to b \times \to c + \to c \times \to a + \to a \times \to b ∣ ∣}{∣ ∣ \to b - \to a ∣ ∣}$

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\to c

\to a

\to b

\frac{∣ ∣ \to b \times \to c + \to c \times \to a + \to a \times \to b ∣ ∣}{∣ ∣ \to b - \to a ∣ ∣}

\to a, \to b, \to c

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α

\to a

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\to a

\to c

β

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(\to a \times \to b) \times (\to b \times \to c) \times (\to c \times \to a)

\to a, \to b, \to c

\to b

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\to a

\to b

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\to a \times (\to b \times \to c) = \frac{1}{2} \to b

\to a

\to b

\to c

\to d

(\to a \times \to b) \times (\to c \times \to d)

\to a

\to b

\to c

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(\to a \times \to b) \times (\to c \times \to d)

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