Maths-
General
Easy
Question
Assertion : For 
the volume of the parallel piped formed by vectors 
and 
is maximum (The vectors form a right-handed system)
Reason: The volume of the parallel piped having three coterminous edges 
and 
- Statement
is true, statement 
is true; statement is a correct explanation for statement
- Statement is true, statement is true statement is not a correct explanation for statement
- Statement is true, statement is false
- statement is false, statement is true
is true, statement is true; statement is a correct explanation for statement
is true, statement is true statement is not a correct explanation for statement
is true, statement is false
is false, statement is true
Hint:
We are given two statements. We have to tell which of the statement is true. For statement 1, we will check if for the given value of "a" the volume is maximum. We will use the formula of volume of parallelepiped. For statement 2, we have to check if parallelepiped have coterminous edges.
The correct answer is: Statement is true, statement is true; statement is a correct explanation for statement
We are given two statements we have to check which of them are true.
Statment 1:
The first statement is about the maximum volume of parallelepiped. We will find the maximum volume of parallelepiped.
We will find the maximum value of parallelepiped.
So, the first statement is true.
Statement 2:
We are getting the maximum value of parallelepiped at this value of a.
Now, we will see statment 2.
Coterminous edges means the vectors or sides end at single common point. So, yes parallelepiped has coterminous edges.
Three edges meet at one point.
As the edges end at one point, we can consider two of them as base. We can take their cross product and take them as base. And, the projection of the third vector with the cross product will give is the height.
Hence the statement 2 is true and a correct explanation of statement 1.
For such questions, we should know the formula of a parallelepiped. We should also know how to take a scalar product.
Related Questions to study
Maths-
Assertion (A): Let 
. If 
such that 
is collinear with 
and 
is perpendicular to is possible, then 
.
Reason (R): If and 
are non-zero, non-collinear vectors, then can be expressed as where is collinear with and is perpendicular to
Assertion (A): Let . If such that is collinear with and is perpendicular to is possible, then .
Reason (R): If and are non-zero, non-collinear vectors, then can be expressed as where is collinear with and is perpendicular to
Maths-General
Maths-
Statement 
If 
are distinct non-negative numbers and the vectors â 
and 
are coplanar then 
is arithmetic mean of 
and 
.
Statement -2: Parallel vectors have proportional direction ratios.
Statement If are distinct non-negative numbers and the vectors â and are coplanar then is arithmetic mean of and .
Statement -2: Parallel vectors have proportional direction ratios.
Maths-General
Maths-
If 
and 
is a vector satisfying 
.
Assertion 
can be expressed in terms of and 
.
Reason 
If and is a vector satisfying .
Assertion can be expressed in terms of and .
Reason
Maths-General
Maths-
If 
are non-zero vectors such that 
then
Assertion 
: Least value of 
is 
Reason (R): The expression 
is least when magnitude of 
is 
If are non-zero vectors such that then
Assertion : Least value of is
Reason (R): The expression is least when magnitude of is
Maths-General
Maths-
Statement- 1: If 
and 
and 
, then there exist real numbers 
, 
such that 
Statement- 2: 
are four vectors in a 3 - dimensional space. If 
are non-coplanar, then there exist real numbers 
such that 
Statement- 1: If and and , then there exist real numbers , such that
Statement- 2: are four vectors in a 3 - dimensional space. If are non-coplanar, then there exist real numbers such that
Maths-General
Maths-
Statement- 
:If 
are non-collinear points. Then every point 
in the plane of 
, can be expressed in the form 
Statement- 
:The condition for coplanarity of four points 
is that there exists scalars 
not all zeros such that 
where 
.
Statement- :If are non-collinear points. Then every point in the plane of , can be expressed in the form
Statement- :The condition for coplanarity of four points is that there exists scalars not all zeros such that where .
Maths-General
Maths-
Assertion (A): The number of vectors of unit length and perpendicular to both the vectors. 
and 
is zero Reason
(R): 
and 
are two non-zero and non-parallel vectors it is true that is perpendicular to the plane containing and
Assertion (A): The number of vectors of unit length and perpendicular to both the vectors. and is zero Reason
(R): and are two non-zero and non-parallel vectors it is true that is perpendicular to the plane containing and
Maths-General
Maths-
The value of 
for which the straight lines 
and 
are coplanar is
For such questions, we should know the condition for two lines to be coplanar. We should also know about the scalar triple product.
The value of for which the straight lines and are coplanar is
Maths-General
For such questions, we should know the condition for two lines to be coplanar. We should also know about the scalar triple product.
Maths-
The position vector of the centre of the circle 
The position vector of the centre of the circle
Maths-General
Maths-
Let 
where 
are three noncoplanar vectors. If 
is perpendicular to 
, then minimum value of 
Let where are three noncoplanar vectors. If is perpendicular to , then minimum value of
Maths-General
Chemistry-
Which of the following represents Westrosol?
Which of the following represents Westrosol?
Chemistry-General
Chemistry-
Which of the following sequences would yield -nitro chlorobenzene (Z) from benzene?
Which of the following sequences would yield -nitro chlorobenzene (Z) from benzene?
Chemistry-General
Chemistry-
For the preparation of chloroethane
For the preparation of chloroethane
Chemistry-General
Chemistry-
Which of the following statements is wrong about the reaction?
Which of the following statements is wrong about the reaction?
Chemistry-General
Chemistry-
In the following reaction, the final product can be prepared by two paths (I) and (II).
Which of the following statements is correct?
In the following reaction, the final product can be prepared by two paths (I) and (II).
Which of the following statements is correct?
Chemistry-General
