The projection of the line segment joining the points (1, –1, 3) and (2, –4, 11) on the line joining the points (–1, 2, 3) and (3, –2, 10) is ____________.

Let A (1, – 1, 3), \(2, – 4, 11), \ (–1, 2, 3) \ (3, –2, 10) \\ AB = i - 3 j + 8 k \\ CD = 4 i - 4 j + 7 k\\ P

The projection of the line segment joining the points 1 1 3 : (Mathematics)

Let $A (1, – 1, 3), \\B(2, – 4, 11), \\C (–1, 2, 3)$ $\\D (3, –2, 10)$ $\\ \therefore \overrightarrow {AB} = \widehat i - 3\widehat j + 8\widehat k$ $\\ \Rightarrow \overrightarrow {CD} = 4\widehat i - 4\widehat j + 7\widehat k\\$ Projection of $\overrightarrow {AB} \text{ on } \overrightarrow {CD}$ $= {{\overrightarrow {AB} .\overrightarrow {CD} } \over {\left| {\overrightarrow {CD} } \right|}}$ $\\ = {{4 + 12 + 56} \over {\sqrt {16 + 16 + 49} }}$ $= {{72} \over 9} = 8$

Explanation

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