JEE MAIN - Mathematics (2020 - 9th January Morning Slot - No. 8)
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
8
Explanation
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 $$\overrightarrow {AB} $$ on $$\overrightarrow {CD} $$ = $${{\overrightarrow {AB} .\overrightarrow {CD} } \over {\left| {\overrightarrow {CD} } \right|}}$$
= $${{4 + 12 + 56} \over {\sqrt {16 + 16 + 49} }}$$
= $${{72} \over 9}$$
= 8
$$ \therefore $$ $$\overrightarrow {AB} = \widehat i - 3\widehat j + 8\widehat k$$
$$ \Rightarrow $$ $$\overrightarrow {CD} = 4\widehat i - 4\widehat j + 7\widehat k$$
Projection of $$\overrightarrow {AB} $$ on $$\overrightarrow {CD} $$ = $${{\overrightarrow {AB} .\overrightarrow {CD} } \over {\left| {\overrightarrow {CD} } \right|}}$$
= $${{4 + 12 + 56} \over {\sqrt {16 + 16 + 49} }}$$
= $${{72} \over 9}$$
= 8
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