Maths-
General
Easy
Question
Assertion : Let 
are position vectors of four points A, B, C & D and 
then points A, B, C and D are coplanar.
Reason : Three non-zero, linearly dependent co-initial vectors (
¸
& 
) are coplanar.
- If both (A) and (R) are true, and (R) is the correct explanation of (A).
- If both (A) and (R) are true but (R) is not the correct explanation of (A).
- If (A) is true but (R) is false.
- If (A) is false but (R) is true.
The correct answer is: If both (A) and (R) are true, and (R) is the correct explanation of (A).
, 
and 
are linearly dependent, hence by reason, assertion is true.
Related Questions to study
Maths-
Assertion : A vector
, directed along the internal bisector of the angle between the vector 
= 7
– 4
– 4
and 
= –2– + 2, with || = 5
is 
(–7+ 2).
Reason : The vector bisecting the angle of & is given by = 
.
Assertion : A vector, directed along the internal bisector of the angle between the vector = 7– 4– 4 and = –2– + 2, with || = 5 is (–7+ 2).
Reason : The vector bisecting the angle of & is given by = .
Maths-General
Maths-
If a, b, c are non-coplanar unit vectors such that a × (b × c) = 
, then the angle between a and b is -
If a, b, c are non-coplanar unit vectors such that a × (b × c) = , then the angle between a and b is -
Maths-General
Maths-
If 
then
If then
Maths-General
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If 
and
are two unit vectors and is the angle between them, then 
If and are two unit vectors and is the angle between them, then
Maths-General
Maths-
Which of the following is a true statement ?
Which of the following is a true statement ?
Maths-General
Maths-
Values of 'x' for which the angle between the vectors 
and 
is obtuse, are
Values of 'x' for which the angle between the vectors and is obtuse, are
Maths-General
Maths-
Let the vectors 
be such that 
. Let P1 and P2 be planes determined by the pairs of vectors 
and 
respectively. Then, then angle between between P1 and P2 is
Let the vectors be such that . Let P1 and P2 be planes determined by the pairs of vectors and respectively. Then, then angle between between P1 and P2 is
Maths-General
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The length of the longest diagonal of the parallelogram constructed on 
and 
if it is given that 
and 
is
The length of the longest diagonal of the parallelogram constructed on and if it is given that and is
Maths-General
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ABCD is a quadrilateral with 
and 
. If its area is times the area of the parallelogram with AB, AD as adjacent sides, then is
ABCD is a quadrilateral with and . If its area is times the area of the parallelogram with AB, AD as adjacent sides, then is
Maths-General
Maths-
Let and 
be non-zero vectors such that 
If is the acute angle between the vectors 
and , then sin equals
Let and be non-zero vectors such that If is the acute angle between the vectors and , then sin equals
Maths-General
Maths-
If 
and 
are three non-coplanar vectors, then 
equals
If and are three non-coplanar vectors, then equals
Maths-General
Maths-
Given two vectors 
and 
, then unit vector coplanar with two vectors and perpendicular to first is
Given two vectors and , then unit vector coplanar with two vectors and perpendicular to first is
Maths-General
Maths-
If vectors 
and 
are the sides of ABC, then the length of the median through A is:
If vectors and are the sides of ABC, then the length of the median through A is:
Maths-General
Maths-
The vectors 
= 
+ 
+ 
and 
= 
– + 
are the sides of a triangle ABC. The length of the median through A is
The vectors = + + and = – + are the sides of a triangle ABC. The length of the median through A is
Maths-General
Maths-
Let , , be distinct real numbers. The points with position vectors 
+ 
+ 
, 
+ 
+ 
, 
+ 
+ 
Let , , be distinct real numbers. The points with position vectors + + , + + , + +
Maths-General
