Maths-
General
Easy
Question
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-1 : If the vector has component P + 2 and 1 with respect to the new system then P = –1
Statement-2 : Magnitude of vector original and new system remains same.
- 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 Statement-1 is false but Statement-2 is true
Related Questions to study
Maths-
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.
Statement I : If three points P, Q, R have position vectorsrespectively 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.
Maths-General
Maths-
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
and new system remains same
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
and new system remains sameMaths-General
Maths-General
Maths-
Assertion: The point of intersection of the lines
Reason : Skew lines do not intersect.
Assertion: The point of intersection of the lines
Reason : Skew lines do not intersect.
Maths-General
Maths-
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
Assertion(A) : k1, 2k2 and k3 are in harmonic progression if P, Q and R are collinear
Reason(R) : Maths-General
Maths-General
Maths-
Assertion(A): If 
then equation 
represent a straight line.
Reason(R): If , then equation 
represent a straight line
Assertion(A): If then equation represent a straight line.
Reason(R): If , then equation represent a straight line
Maths-General
Maths-
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.
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.
Maths-General
Maths-
Assertion: If 
× 
= 
× 
, and ×= × then – is perpendicular to –.
Reason: If 
is perpendicular to
then .= 0
Assertion: If × = × , and ×= × then – is perpendicular to –.
Reason: If is perpendicular tothen .= 0
Maths-General
Maths-
Assertion: Vectors – 2
+
+ 
, –+and + –2 are coplanar for only two values of .
Reason: Three vectors 
, 
, 
are coplanar if .(× ) = 
.
Assertion: Vectors – 2+ + , –+and + –2 are coplanar for only two values of .
Reason: Three vectors , , are coplanar if .(× ) = .
Maths-General
Maths-
Assertion (A): If vector and are linearly dependent, then vectors , , must be dependent.
Reason (R): If vector and are linearly independent, then vectors , , must be linearly independent, where vector is non-zero.
Assertion (A): If vector and are linearly dependent, then vectors , , must be dependent.
Reason (R): If vector and are linearly independent, then vectors , , must be linearly independent, where vector is non-zero.
Maths-General
Maths-
Assertion: If in a ABC ; 
= 
– 
and 
= 
; |
| |
|, then the value of cos 2A + cos 2B + cos 2C is – 1.
Reason: If in ABC, C = 90º, then cos 2A + cos 2B + cos 2C = – 1.
Assertion: If in a ABC ; = – and = ; || ||, then the value of cos 2A + cos 2B + cos 2C is – 1.
Reason: If in ABC, C = 90º, then cos 2A + cos 2B + cos 2C = – 1.Maths-General
Maths-General
Maths-
If 
are noncoplanar vectors and 
.
Assertion: and are linearly dependent
Reason: 
is r to each of three 
.
If are noncoplanar vectors and .
Assertion: and are linearly dependent
Reason: is r to each of three .
Maths-General
Maths-
Maths-General
Maths-General
Maths-
Assertion(A) : If then equation represent a straight line.
Reason(R) : If , then equation represent a straight line
Assertion(A) : If then equation represent a straight line.
Reason(R) : If , then equation represent a straight line
Maths-General
Maths-
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.
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.
Maths-General
Maths-
Assertion : If × = × , and ×= × then – is perpendicular to –.
Reason : If is perpendicular tothen .= 0
Assertion : If × = × , and ×= × then – is perpendicular to –.
Reason : If is perpendicular tothen .= 0
Maths-General
