JEE MAIN - Mathematics (2021 - 25th February Morning Shift - No. 2)
The equation of the line through the point (0, 1, 2) and perpendicular to the line
$${{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over { - 2}}$$ is :
$${{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over { - 2}}$$ is :
$${x \over 3} = {{y - 1} \over { - 4}} = {{z - 2} \over 3}$$
$${x \over 3} = {{y - 1} \over 4} = {{z - 2} \over { - 3}}$$
$${x \over { - 3}} = {{y - 1} \over 4} = {{z - 2} \over 3}$$
$${x \over 3} = {{y - 1} \over 4} = {{z - 2} \over 3}$$
Explanation
$${{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over { - 2}} = \lambda $$
Any point on this line $$(2\lambda + 1,3\lambda - 1, - 2\lambda + 1)$$
_25th_February_Morning_Shift_en_2_1.png)
Direction ratio of given line $$(2,3, - 2)$$
Direction ratio of line to be found $$(2\lambda + 1,3\lambda - 2, - 2\lambda - 1)$$
$$ \therefore $$ $${\overrightarrow d _1}\,.\,{\overrightarrow d _2} = 0$$
$$ \Rightarrow $$ $$\lambda = 2/17$$
Direction ratio of line $$(21, - 28, - 21) \equiv (3, - 4, - 3) \equiv ( - 3,4,3)$$
Any point on this line $$(2\lambda + 1,3\lambda - 1, - 2\lambda + 1)$$
Direction ratio of given line $$(2,3, - 2)$$
Direction ratio of line to be found $$(2\lambda + 1,3\lambda - 2, - 2\lambda - 1)$$
$$ \therefore $$ $${\overrightarrow d _1}\,.\,{\overrightarrow d _2} = 0$$
$$ \Rightarrow $$ $$\lambda = 2/17$$
Direction ratio of line $$(21, - 28, - 21) \equiv (3, - 4, - 3) \equiv ( - 3,4,3)$$
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