Consider the planes 3x andndash; 6y andndash; 2z = 15 and 2x + y andndash; 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. becauseSTATEMENT-2 : The vector 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-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 True.Correct answer is option 'D'. Can you explain this answer?

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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. because

STATEMENT-2 : The vector

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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Test: Comprehension Based Questions: Vector Algebra and Three Dimensional Geometry

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Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2...

The line of intersection of given plane is 3x -6y - 2z -15 = 0 = 2x + y - 2z-5
For z = 0 , we obtain x = 3 and y =-1
∴Line passes through (3, –1, 0).
Let a, b, c be the d’rs of line of intersection, then 3a -6b -2c = 0 and 2a + b - 2c = 0

Solving the above equations using cross product method, we get a :b :c = 14 : 2 : 15

∴ Eqn. of line is

whose parametric form is x = 3 + 14t , y = 1 + 2t, z= 15t

∴ Statement-I is false (value of y is not matching).
Since dr’s of line intersection of given planes are 14, 2,15

∴

is parallel to this line.
∴ Statement 2 is true.

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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. becauseSTATEMENT-2 : The vector 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-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 True.Correct answer is option 'D'. Can you explain this answer?

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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. becauseSTATEMENT-2 : The vector 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-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 True.Correct 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 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. becauseSTATEMENT-2 : The vector 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-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 True.Correct 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 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. becauseSTATEMENT-2 : The vector 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-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 True.Correct answer is option 'D'. Can you explain this answer?.

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