JEE MAIN - Mathematics (2020 - 7th January Evening Slot - No. 9)
If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through ($$\alpha $$, 7, 1)
is
$$\left( {{5 \over 3},{7 \over 3},{{17} \over 3}} \right)$$, then $$\alpha $$ is equal to______.
Answer
4
Explanation
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Direction Ratio of PQ are
= ($${5 \over 3} - 1$$, $${7 \over 3} - 0$$, $${{17} \over 3} - 3$$)
= (2, 7, 8)
Direction ratio of line QA are
= ($$\alpha - {5 \over 3}$$, $$7 - {7 \over 3}$$, 1 - $${{17} \over 3}$$)
= (3$$\alpha $$ – 5, 14, –14)
PQ is perpendicular to line QA
$$ \therefore $$ $$\overrightarrow {PQ} .\overrightarrow {QA} $$ = 0
$$ \Rightarrow $$ 2(3$$\alpha $$ – 5) + 7.14 + (–14).8 = 0
$$ \Rightarrow $$ $$\alpha $$ = 4
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