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In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-
Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.
Statement-1:
The parametric equations of the line of intersection of the given planes are
x = 3 + 14t, y = 1 + 2t, z = 15t.
Statement-2:
The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planes
Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.
Statement-1:
The parametric equations of the line of intersection of the given planes are
x = 3 + 14t, y = 1 + 2t, z = 15t.
Statement-2:
The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planes
- a)Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
- b)Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1
- c)Statement-1 is True, Statement-2 is False
- d)Statement-1 is False, Statement-2 is True
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In the following question, a Statement-1 is given followed by a corres...
Statement-1 :Line of intersection of given planes is given by,L = 3x - 6y - 2z - 15 + t(2x + y - 2z - 5) = 0L = (3 + 2t)x + (t - 6)y - 2(1 + t)z - 5(t + 3) = 0So, the parametric equations of the line are: x = 2t + 3, y = t - 6, z = -2(t + 1) Statement-2 :Equation of normal for plane 1 : 3i - 6j - 2kEquation of normal for plane 2 : 2i + j - 2kFor a line to be parallel to the line of intersection of planes then it must be perpendicular to the normal's of the planes. Given line is 14i = 2j = 15k(14i + 2j + 15k)•(3i - 6j - 2k) = 42 - 12 - 30 = 0(14i +2j + 15k)•(2i + j - 2k) = 28 + 2 - 30 = 0Since the dot product's are zero the given line is parallel to the line of intersection of planes.
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In the following question, a Statement-1 is given followed by a corres...
Statement-1: The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.
Statement-2: The vector 14î + 2ĵ + 15k̂ is parallel to the line of intersection of given planes.
Explanation:
The given planes are:
1) 3x – 6y – 2z = 15
2) 2x + y – 2z = 5
To find the line of intersection of these planes, we can solve the given equations simultaneously.
Solving the system of equations:
First, we can write the equations of the planes in the matrix form as:
| 3 -6 -2 | | x | | 15 |
| 2 1 -2 | * | y | = | 5 |
Using Gaussian elimination or other methods, we can solve the system of equations to find the values of x, y, and z.
After solving, we get x = 3 + 14t, y = 1 + 2t, and z = 15t where t is a parameter.
Parametric equations of the line of intersection:
The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.
Vector parallel to the line of intersection:
To check if the vector 14î + 2ĵ + 15k̂ is parallel to the line of intersection, we can compare the direction ratios.
The direction ratios of the vector 14î + 2ĵ + 15k̂ are 14, 2, and 15.
Comparing these ratios with the coefficients of x, y, and z in the parametric equations, we can see that they are the same. Therefore, the vector 14î + 2ĵ + 15k̂ is parallel to the line of intersection of the given planes.
Conclusion:
Hence, both Statement-1 and Statement-2 are true. However, Statement-2 is not a correct explanation for Statement-1 as it only confirms that the vector is parallel to the line of intersection, but it does not explain how the parametric equations are obtained. Therefore, the correct answer is option D.
Statement-2: The vector 14î + 2ĵ + 15k̂ is parallel to the line of intersection of given planes.
Explanation:
The given planes are:
1) 3x – 6y – 2z = 15
2) 2x + y – 2z = 5
To find the line of intersection of these planes, we can solve the given equations simultaneously.
Solving the system of equations:
First, we can write the equations of the planes in the matrix form as:
| 3 -6 -2 | | x | | 15 |
| 2 1 -2 | * | y | = | 5 |
Using Gaussian elimination or other methods, we can solve the system of equations to find the values of x, y, and z.
After solving, we get x = 3 + 14t, y = 1 + 2t, and z = 15t where t is a parameter.
Parametric equations of the line of intersection:
The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.
Vector parallel to the line of intersection:
To check if the vector 14î + 2ĵ + 15k̂ is parallel to the line of intersection, we can compare the direction ratios.
The direction ratios of the vector 14î + 2ĵ + 15k̂ are 14, 2, and 15.
Comparing these ratios with the coefficients of x, y, and z in the parametric equations, we can see that they are the same. Therefore, the vector 14î + 2ĵ + 15k̂ is parallel to the line of intersection of the given planes.
Conclusion:
Hence, both Statement-1 and Statement-2 are true. However, Statement-2 is not a correct explanation for Statement-1 as it only confirms that the vector is parallel to the line of intersection, but it does not explain how the parametric equations are obtained. Therefore, the correct answer is option D.
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In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.Statement-1:The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.Statement-2:The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planesa)Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer?
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In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.Statement-1:The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.Statement-2:The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planesa)Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.Statement-1:The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.Statement-2:The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planesa)Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.Statement-1:The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.Statement-2:The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planesa)Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer?.
In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.Statement-1:The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.Statement-2:The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planesa)Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.Statement-1:The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.Statement-2:The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planesa)Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.Statement-1:The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.Statement-2:The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planesa)Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer?.
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