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A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given by
- a)(2a, 3a, 3a), (2a, a, a)
- b)(3a, 2a, 3a), (a, a, a)
- c)(3a, 2a, 3a), (a, a, 2a)
- d)(3a, 3a, 3a), (a, a, a)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A line with direction cosines proportional to 2, 1, 2 meets each of th...
IT'S SIMPLE!!!!
The direction cosines are proportional to 2,1,2.
The difference of the points of intersection will give the direction ratios. So, subtract the the points of intersection given in the options. In option B , the direction ratios obtained are (2a,a,2a). Here it's easy to see from the direction ratios obtained that the direction cosines of this line will be proportional to 2,1,2.
Hence B is the correct answer.
I hope you have got it. If not then u can discuss it with me.
The direction cosines are proportional to 2,1,2.
The difference of the points of intersection will give the direction ratios. So, subtract the the points of intersection given in the options. In option B , the direction ratios obtained are (2a,a,2a). Here it's easy to see from the direction ratios obtained that the direction cosines of this line will be proportional to 2,1,2.
Hence B is the correct answer.
I hope you have got it. If not then u can discuss it with me.
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Community Answer
A line with direction cosines proportional to 2, 1, 2 meets each of th...
To find the coordinates of the points of intersection, we need to solve the given equations simultaneously.
Given information:
Direction cosines of the line = 2, 1, 2
Equations of the lines:
1. x = y
2. a = z
3. x = 2y = 2z
Let's solve these equations one by one:
1. x = y
Substitute x = y in equation 3.
y = 2y = 2z
Divide the equation by y to get:
1 = 2 = 2z/y
Simplifying, we get:
z = y/2
Substitute the value of z in equation 2:
a = y/2
So, the coordinates of the point of intersection of the line with equation 1 and equation 2 are (y, y/2, a).
2. a = z
Substitute a = z in equation 3.
x = 2y = 2a
Divide the equation by 2 to get:
x/2 = y/2 = a
So, the coordinates of the point of intersection of the line with equation 1 and equation 2 are (x/2, y/2, y/2).
3. x = 2y = 2z
Substitute x = 2y = 2z in equation 1.
2y = y
y = 0
Substitute y = 0 in equation 2.
a = 0
So, the coordinates of the point of intersection of the line with equation 1 and equation 2 are (0, 0, 0).
From the above calculations, we can see that the coordinates of the points of intersection are given by (y, y/2, a), (x/2, y/2, y/2), and (0, 0, 0).
Comparing these coordinates with the given options, we can see that option B, (3a, 2a, 3a), (a, a, a), matches with the calculated coordinates.
Hence, the correct answer is option B.
Given information:
Direction cosines of the line = 2, 1, 2
Equations of the lines:
1. x = y
2. a = z
3. x = 2y = 2z
Let's solve these equations one by one:
1. x = y
Substitute x = y in equation 3.
y = 2y = 2z
Divide the equation by y to get:
1 = 2 = 2z/y
Simplifying, we get:
z = y/2
Substitute the value of z in equation 2:
a = y/2
So, the coordinates of the point of intersection of the line with equation 1 and equation 2 are (y, y/2, a).
2. a = z
Substitute a = z in equation 3.
x = 2y = 2a
Divide the equation by 2 to get:
x/2 = y/2 = a
So, the coordinates of the point of intersection of the line with equation 1 and equation 2 are (x/2, y/2, y/2).
3. x = 2y = 2z
Substitute x = 2y = 2z in equation 1.
2y = y
y = 0
Substitute y = 0 in equation 2.
a = 0
So, the coordinates of the point of intersection of the line with equation 1 and equation 2 are (0, 0, 0).
From the above calculations, we can see that the coordinates of the points of intersection are given by (y, y/2, a), (x/2, y/2, y/2), and (0, 0, 0).
Comparing these coordinates with the given options, we can see that option B, (3a, 2a, 3a), (a, a, a), matches with the calculated coordinates.
Hence, the correct answer is option B.
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A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given bya)(2a, 3a, 3a), (2a, a, a)b)(3a, 2a, 3a), (a, a, a)c)(3a, 2a, 3a), (a, a, 2a)d)(3a, 3a, 3a), (a, a, a)Correct answer is option 'B'. Can you explain this answer?
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A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given bya)(2a, 3a, 3a), (2a, a, a)b)(3a, 2a, 3a), (a, a, a)c)(3a, 2a, 3a), (a, a, 2a)d)(3a, 3a, 3a), (a, a, a)Correct answer is option 'B'. 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 A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given bya)(2a, 3a, 3a), (2a, a, a)b)(3a, 2a, 3a), (a, a, a)c)(3a, 2a, 3a), (a, a, 2a)d)(3a, 3a, 3a), (a, a, a)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given bya)(2a, 3a, 3a), (2a, a, a)b)(3a, 2a, 3a), (a, a, a)c)(3a, 2a, 3a), (a, a, 2a)d)(3a, 3a, 3a), (a, a, a)Correct answer is option 'B'. Can you explain this answer?.
A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given bya)(2a, 3a, 3a), (2a, a, a)b)(3a, 2a, 3a), (a, a, a)c)(3a, 2a, 3a), (a, a, 2a)d)(3a, 3a, 3a), (a, a, a)Correct answer is option 'B'. 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 A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given bya)(2a, 3a, 3a), (2a, a, a)b)(3a, 2a, 3a), (a, a, a)c)(3a, 2a, 3a), (a, a, 2a)d)(3a, 3a, 3a), (a, a, a)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given bya)(2a, 3a, 3a), (2a, a, a)b)(3a, 2a, 3a), (a, a, a)c)(3a, 2a, 3a), (a, a, 2a)d)(3a, 3a, 3a), (a, a, a)Correct answer is option 'B'. Can you explain this answer?.
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