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 ____________.
Answer (integer)
8
Solution
Let A (1, – 1, 3), B(2, – 4, 11), C (–1, 2, 3) & D (3, –2, 10)
<br><br>$\therefore$ $\overrightarrow {AB} = \widehat i - 3\widehat j + 8\widehat k$
<br><br>$\Rightarrow$ $\overrightarrow {CD} = 4\widehat i - 4\widehat j + 7\widehat k$
<br><br>Projection of $\overrightarrow {AB}$ on $\overrightarrow {CD}$ = $${{\overrightarrow {AB} .\overrightarrow {CD} } \over {\left| {\overrightarrow {CD} } \right|}}$$
<br><br> = ${{4 + 12 + 56} \over {\sqrt {16 + 16 + 49} }}$
<br><br> = ${{72} \over 9}$
<br><br> = 8
About this question
Subject: Mathematics · Chapter: Three Dimensional Geometry · Topic: Direction Cosines and Ratios
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