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The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =
- a)77/121
- b)-32/121
- c)77
- d)85/121
Correct answer is option 'A'. Can you explain this answer?
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The d.r’s of the line AB are 6, - 2,9. If the line AB makes angl...
a, b, c = 6, -2, 9
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The d.r’s of the line AB are 6, - 2,9. If the line AB makes angl...
To solve this question, we need to find the direction ratios of the line AB and then use the given angles to find the values of sin2 and sin2.
Finding the Direction Ratios of Line AB:
The direction ratios of a line can be found by taking the differences between the coordinates of two points on the line. In this case, we are given the direction ratios of line AB as 6, -2, and 9.
Finding the Values of sin2 and sin2:
We are given that the line AB makes angles , with oy and oz respectively. To find the values of sin2 and sin2, we need to use the trigonometric ratios.
The trigonometric ratios for a right-angled triangle can be defined as follows:
- sin = opposite/hypotenuse
- cos = adjacent/hypotenuse
- tan = opposite/adjacent
Let's consider the angle with oy first. The angle with oy forms a right-angled triangle with AB as the hypotenuse. The opposite side of the angle is the y-coordinate of AB, which is -2. The hypotenuse is the magnitude of AB, which can be calculated using the direction ratios.
The magnitude of AB = sqrt(6^2 + (-2)^2 + 9^2) = sqrt(36 + 4 + 81) = sqrt(121) = 11
Using the trigonometric ratio sin = opposite/hypotenuse, we can calculate sin2 as:
sin2 = (-2)/11 = -2/11
Similarly, let's consider the angle with oz. The angle with oz forms a right-angled triangle with AB as the hypotenuse. The opposite side of the angle is the z-coordinate of AB, which is 9.
Using the magnitude of AB calculated earlier, we can calculate sin2 as:
sin2 = 9/11
Calculating the Difference:
Now, we need to find the difference sin2 - sin2:
sin2 - sin2 = (-2/11) - (9/11) = -11/11 = -1
The correct answer is option 'A', which represents -1.
Finding the Direction Ratios of Line AB:
The direction ratios of a line can be found by taking the differences between the coordinates of two points on the line. In this case, we are given the direction ratios of line AB as 6, -2, and 9.
Finding the Values of sin2 and sin2:
We are given that the line AB makes angles , with oy and oz respectively. To find the values of sin2 and sin2, we need to use the trigonometric ratios.
The trigonometric ratios for a right-angled triangle can be defined as follows:
- sin = opposite/hypotenuse
- cos = adjacent/hypotenuse
- tan = opposite/adjacent
Let's consider the angle with oy first. The angle with oy forms a right-angled triangle with AB as the hypotenuse. The opposite side of the angle is the y-coordinate of AB, which is -2. The hypotenuse is the magnitude of AB, which can be calculated using the direction ratios.
The magnitude of AB = sqrt(6^2 + (-2)^2 + 9^2) = sqrt(36 + 4 + 81) = sqrt(121) = 11
Using the trigonometric ratio sin = opposite/hypotenuse, we can calculate sin2 as:
sin2 = (-2)/11 = -2/11
Similarly, let's consider the angle with oz. The angle with oz forms a right-angled triangle with AB as the hypotenuse. The opposite side of the angle is the z-coordinate of AB, which is 9.
Using the magnitude of AB calculated earlier, we can calculate sin2 as:
sin2 = 9/11
Calculating the Difference:
Now, we need to find the difference sin2 - sin2:
sin2 - sin2 = (-2/11) - (9/11) = -11/11 = -1
The correct answer is option 'A', which represents -1.
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The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =a)77/121b)-32/121c)77d)85/121Correct answer is option 'A'. Can you explain this answer?
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The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =a)77/121b)-32/121c)77d)85/121Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =a)77/121b)-32/121c)77d)85/121Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =a)77/121b)-32/121c)77d)85/121Correct answer is option 'A'. Can you explain this answer?.
The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =a)77/121b)-32/121c)77d)85/121Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =a)77/121b)-32/121c)77d)85/121Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =a)77/121b)-32/121c)77d)85/121Correct answer is option 'A'. Can you explain this answer?.
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The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =a)77/121b)-32/121c)77d)85/121Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =a)77/121b)-32/121c)77d)85/121Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The d.r’s of the line AB are 6, - 2,9. If the line AB makes angles α,β with oy, oz respectively where O = ( 0, 0, 0) then sin2α - sin2β =a)77/121b)-32/121c)77d)85/121Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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