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If are three non-collinear points with position vectors , respectively, then show that the length…
If $A, B, C$ are three non-collinear points with position vectors $\vec{a}, \vec{b}, \vec{c}$, respectively, then show that the length of the perpendicular from $C$ on $AB$ is $\frac{|(\vec{a} \times \vec{b}) + (\vec{b} \times \vec{c}) + (\vec{c} \times \vec{a})|}{|\vec{b} - \vec{a}|}$.
Given: $A, B, C$ are three non-collinear points with position vectors $\vec{a}, \vec{b}, \vec{c}$, respectively
To show: Length of the perpendicular from $C$ on $AB$ is $\frac{|(\vec{a} \times \vec{b}) + (\vec{b} \times \vec{c}) + (\vec{c} \times \vec{a})|}{|\vec{b} - \vec{a}|}$
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From ISC 2018 Mathematics Paper 1, question 16(a).