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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as
Assertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.
Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false but R is True
Correct answer is option 'C'. Can you explain this answer?
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Direction: In the following questions, A statement of Assertion (A) i...
Assertion (A) is correct.
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Since P = (5, y, z)
Equation of line joining (3, 2, –1) and (6, –4, –2) is
so if point P lies on the line then it must satisfy the above equation
Hence y co-ordinate of P is –2.
Reason (R) is false.
Since, the two lines x = ay + b, z = cy + d and = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + cc’ + 1 = 0.
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Direction: In the following questions, A statement of Assertion (A) i...
Assertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.
Reason (R): The two lines x = ay b, z = cy d and x = a’y b’, z = c’y d’ will be perpendicular, iff aa’ bb’ cc’ = 0.
The given assertion relates to the coordinates of a point P on a line segment joining two given points. The reason provided relates to the condition for two lines to be perpendicular.
Explanation:
To understand this assertion and reason, let's first find the equation of the line segment joining the points (3, 2, –1) and (6, –4, –2).
The equation of a line segment joining two points (x₁, y₁, z₁) and (x₂, y₂, z₂) can be written as:
(x - x₁)/(x₂ - x₁) = (y - y₁)/(y₂ - y₁) = (z - z₁)/(z₂ - z₁)
Plugging in the given values, we have:
(x - 3)/(6 - 3) = (y - 2)/(-4 - 2) = (z + 1)/(-2 - (-1))
Simplifying, we get:
(x - 3)/3 = (y - 2)/(-6) = (z + 1)/(-1)
Now, let's consider the x-coordinate of P as 5. Substituting this value into the equation, we get:
(5 - 3)/3 = (y - 2)/(-6) = (z + 1)/(-1)
2/3 = (y - 2)/(-6) = (z + 1)/(-1)
Simplifying further, we get:
(y - 2)/(-6) = (z + 1)/(-1)
Cross-multiplying, we get:
-6(y - 2) = -1(z + 1)
Expanding, we get:
-6y + 12 = -z - 1
Rearranging, we get:
z = -6y + 13
Comparing this equation with the given equations:
x = ay + b
z = cy + d
We can see that a = 0, b = 0, c = -6, and d = 13.
Now, let's consider the given reason. According to the reason, the two lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' will be perpendicular if aa' + bb' + cc' = 0.
Plugging in the values, we have:
(0)(0) + (0)(0) + (-6)(0) = 0
Therefore, aa' + bb' + cc' = 0, which means the two lines are perpendicular.
Therefore, both the assertion and the reason are true, and the reason correctly explains the assertion.
Hence, the correct answer is option C.
Reason (R): The two lines x = ay b, z = cy d and x = a’y b’, z = c’y d’ will be perpendicular, iff aa’ bb’ cc’ = 0.
The given assertion relates to the coordinates of a point P on a line segment joining two given points. The reason provided relates to the condition for two lines to be perpendicular.
Explanation:
To understand this assertion and reason, let's first find the equation of the line segment joining the points (3, 2, –1) and (6, –4, –2).
The equation of a line segment joining two points (x₁, y₁, z₁) and (x₂, y₂, z₂) can be written as:
(x - x₁)/(x₂ - x₁) = (y - y₁)/(y₂ - y₁) = (z - z₁)/(z₂ - z₁)
Plugging in the given values, we have:
(x - 3)/(6 - 3) = (y - 2)/(-4 - 2) = (z + 1)/(-2 - (-1))
Simplifying, we get:
(x - 3)/3 = (y - 2)/(-6) = (z + 1)/(-1)
Now, let's consider the x-coordinate of P as 5. Substituting this value into the equation, we get:
(5 - 3)/3 = (y - 2)/(-6) = (z + 1)/(-1)
2/3 = (y - 2)/(-6) = (z + 1)/(-1)
Simplifying further, we get:
(y - 2)/(-6) = (z + 1)/(-1)
Cross-multiplying, we get:
-6(y - 2) = -1(z + 1)
Expanding, we get:
-6y + 12 = -z - 1
Rearranging, we get:
z = -6y + 13
Comparing this equation with the given equations:
x = ay + b
z = cy + d
We can see that a = 0, b = 0, c = -6, and d = 13.
Now, let's consider the given reason. According to the reason, the two lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' will be perpendicular if aa' + bb' + cc' = 0.
Plugging in the values, we have:
(0)(0) + (0)(0) + (-6)(0) = 0
Therefore, aa' + bb' + cc' = 0, which means the two lines are perpendicular.
Therefore, both the assertion and the reason are true, and the reason correctly explains the assertion.
Hence, the correct answer is option C.
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'C'. Can you explain this answer?
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'C'. 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'C'. Can you explain this answer?.
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'C'. 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice asAssertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is TrueCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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