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Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is
(A) (6, 6, 3)
(B) (1, 4, 8)
(C) (3, 6, 6)
(D) (1, √40, √40)?
(A) (6, 6, 3)
(B) (1, 4, 8)
(C) (3, 6, 6)
(D) (1, √40, √40)?
Most Upvoted Answer
Let 1, 2 and 2 be the direction ratios of a straight line passing thro...
Solution:
Given direction ratios are 1, 2 and 2.
Let the point on the line be (x, y, z).
Then the direction ratios of the line passing through the origin and (x, y, z) are x, y and z.
Using the condition that these direction ratios are proportional to 1, 2 and 2, we get
x/1 = y/2 = z/2
Let k be the common ratio.
Then x = k, y = 2k and z = 2k.
The equation of the line passing through the origin and (x, y, z) is given by
x/1 = y/2 = z/2 = t, where t is a parameter.
Eliminating t, we get
x = t, y = 2t and z = 2t.
The distance between the origin and (x, y, z) is given by
√(x^2 + y^2 + z^2) = √(t^2 + 4t^2 + 4t^2) = √(9t^2) = 3|t|.
Therefore, |t| = 3.
Taking t = 3, we get the point (3, 6, 6).
Taking t = -3, we get the point (-3, -6, -6).
Therefore, the possible points on the line at a distance 9 from the origin are (3, 6, 6) and (-3, -6, -6).
Option (C) (1, 4, 8) is not on the line.
Option (D) (1, √40, √40) is not at a distance 9 from the origin.
Therefore, the answer is (A) (6, 6, 3).
Given direction ratios are 1, 2 and 2.
Let the point on the line be (x, y, z).
Then the direction ratios of the line passing through the origin and (x, y, z) are x, y and z.
Using the condition that these direction ratios are proportional to 1, 2 and 2, we get
x/1 = y/2 = z/2
Let k be the common ratio.
Then x = k, y = 2k and z = 2k.
The equation of the line passing through the origin and (x, y, z) is given by
x/1 = y/2 = z/2 = t, where t is a parameter.
Eliminating t, we get
x = t, y = 2t and z = 2t.
The distance between the origin and (x, y, z) is given by
√(x^2 + y^2 + z^2) = √(t^2 + 4t^2 + 4t^2) = √(9t^2) = 3|t|.
Therefore, |t| = 3.
Taking t = 3, we get the point (3, 6, 6).
Taking t = -3, we get the point (-3, -6, -6).
Therefore, the possible points on the line at a distance 9 from the origin are (3, 6, 6) and (-3, -6, -6).
Option (C) (1, 4, 8) is not on the line.
Option (D) (1, √40, √40) is not at a distance 9 from the origin.
Therefore, the answer is (A) (6, 6, 3).
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Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is(A) (6, 6, 3) (B) (1, 4, 8) (C) (3, 6, 6) (D) (1, √40, √40)?
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Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is(A) (6, 6, 3) (B) (1, 4, 8) (C) (3, 6, 6) (D) (1, √40, √40)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is(A) (6, 6, 3) (B) (1, 4, 8) (C) (3, 6, 6) (D) (1, √40, √40)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is(A) (6, 6, 3) (B) (1, 4, 8) (C) (3, 6, 6) (D) (1, √40, √40)?.
Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is(A) (6, 6, 3) (B) (1, 4, 8) (C) (3, 6, 6) (D) (1, √40, √40)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is(A) (6, 6, 3) (B) (1, 4, 8) (C) (3, 6, 6) (D) (1, √40, √40)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is(A) (6, 6, 3) (B) (1, 4, 8) (C) (3, 6, 6) (D) (1, √40, √40)?.
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Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is(A) (6, 6, 3) (B) (1, 4, 8) (C) (3, 6, 6) (D) (1, √40, √40)?, a detailed solution for Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is(A) (6, 6, 3) (B) (1, 4, 8) (C) (3, 6, 6) (D) (1, √40, √40)? has been provided alongside types of Let 1, 2 and 2 be the direction ratios of a straight line passing through the origin. Then the coordinates of a point on this line at a distance 9 from the origin is(A) (6, 6, 3) (B) (1, 4, 8) (C) (3, 6, 6) (D) (1, √40, √40)? theory, EduRev gives you an
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