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), B(2, – 4, 11), C (–1, 2, 3) D (3, –2, 10) \ Therefore -> AB = hat i - 3hat j + 8hat k \ => -> CD = 4hat i - 4hat j + 7hat k Projection of -> AB on -> CD = -> AB .-> CD / | -> CD | \ = 4 + 12 + 56 / sqrt 16 + 16 + 49 = 72 / 9 = 8

The projection of the line segment joining the points 1... | (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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