Maths-
General
Easy
Question
Statement I : If three points P, Q, R have position vectors
respectively and
, then the points P, Q, R must be collinear.
Statement II : If for three points A, B, C, ; 
, then the points A, B, C must be collinear.
- If both Statement-1 and Statement-2 are true and the Statement-2 is correct explanation of the Statement-1.
- If both Statement-1 and Statement-2 are true but Statement-2 is not correct explanation of the Statement-1.
- If Statement-1 is true but the Statement-2 is false.
- If Statement-1 is false but Statement-2 is true
The correct answer is: If both Statement-1 and Statement-2 are true and the Statement-2 is correct explanation of the Statement-1.
must be parallel since there is common point A. The points A, B , C must be collinear.
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A vector has components p and 1 with respect to a rectangular Cartesian system. If the axes are rotated through an angle about the origin in the anticlockwise sense.
Statement I : If the vector has component p + 2 and 1 with respect to the new system then p = –1
Statement II : Magnitude of vector with original
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Let P, Q and R are points on sides AB, AC and AD of the parallelogram ABCD such that 
and 
, where k1, k2 and k3 are non-zero positive scalars
Assertion(A) : k1, 2k2 and k3 are in harmonic progression if P, Q and R are collinear
Reason(R) : 
Let P, Q and R are points on sides AB, AC and AD of the parallelogram ABCD such that and , where k1, k2 and k3 are non-zero positive scalars
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Assertion(A): Let 
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Assertion: Vectors – 2
+
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, –+and + –2 are coplanar for only two values of .
Reason: Three vectors 
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, 
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Assertion: Vectors – 2+ + , –+and + –2 are coplanar for only two values of .
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Assertion (A): If vector and are linearly dependent, then vectors , , must be dependent.
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Assertion: If in a ABC ; 
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– 
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; |
| |
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If 
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.
Assertion: and are linearly dependent
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If are noncoplanar vectors and .
Assertion: and are linearly dependent
Reason: is r to each of three .
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Reason(R) : If , then equation represent a straight line
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Assertion(A) : Let and be three points such that and then OABC is a tetrahedron.
Reason(R) : Let and be three points such that are non-coplanar, then OABC is a tetrahedron, where O is the origin.
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Reason : If is perpendicular tothen .= 0
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Reason : If is perpendicular tothen .= 0
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Assertion : Vectors – 2+ + , –+and + –2 are coplanar for only two values of .
Reason : Three vectors , , are coplanar if .(× ) = .
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