GATE CS 2020 Set 1 — Question 9
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
Two straight lines are drawn perpendicular to each other in X-Y plane. If and are the acute angles the straight lines make with the X-axis, then is ______.
Correct answer
(B) 90^()
Solution
Let the two lines be and .
Since they are perpendicular, the difference between their angles of inclination is .
Let the inclination of be (where ).
Then the inclination of must be (or ).The question asks for and , which are the acute angles the lines make with the X-axis.
For , the angle with the X-axis is . Since it is acute, .
For , the inclination is . This is an obtuse angle (since ).
The acute angle makes with the X-axis is .
So, .We need to find :
.Thus, the sum is .
Since they are perpendicular, the difference between their angles of inclination is .
Let the inclination of be (where ).
Then the inclination of must be (or ).The question asks for and , which are the acute angles the lines make with the X-axis.
For , the angle with the X-axis is . Since it is acute, .
For , the inclination is . This is an obtuse angle (since ).
The acute angle makes with the X-axis is .
So, .We need to find :
.Thus, the sum is .
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