Let the volume of a parallelopiped whose coterminous edges are given by and
be 1 cu. unit. If
be the angle between the edges
and
then
can be :
Option: 1
Option: 2
Option: 3
Option: 4
Dot (Scalar) Product in Terms of Components -
Angle between two vectors
-
Geometrical Interpretation of Scalar Triple Product -
Let vectors and
represented the sides of a parallelepiped OA, OB and OC respectively. Then,
is a vector perpendicular to the plane of
and
. Let ? be the angle between vectors
and
and α be the angle between
and
.
If is a unit vector along
, then α is the angle between
and
.
-
Correct Option (3)
View Full Answer(1)Let and
be two vectors. If
is a vector such that
and
then
is equal to :
Option: 1
Option: 2
Option: 3
Option: 4
Vector Triple Product -
For three vectors and
vector triple product is defined as
.
-
Correct Option (3)
View Full Answer(1)Let and
be three unit vectors such that
.If
and
then the ordered pair,
is equal to :
Option: 1
Option:2
Option: 3
Option: 4
Addition and subtraction of Vectors -
Properties of vector addition
The sum of two vectors is always a vector.
Properties of vector Subtraction
-
Correct Option (3)
View Full Answer(1)Let be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle
, with the vector
. Then
is equal to ________.
Given,
and these are mutually perpendicular,
So,
Angle of with
Now,
Using this in (i)
Hence, the correct answer is 4
View Full Answer(1)Study 40% syllabus and score up to 100% marks in JEE
Let . Let a vector
be in the plane containing
. If
is perpendicular to the vector
and its projection on
is 19 units, then
is equal to___________
(a vector in the plane of &
and perpendicular to
)
Give expression is
OR
option (4)
...............(1)
..........(2)
From (1) and (2)
So
Also
So
Angle
Let be three vectors such that,
is perpendicular to
. Then the greatest amongst the values of
is__________
If the projection of the vector on the sum of the two vectors
and
is 1, then
is equal to ________.
Sum of vectors ( ) is
Projection of on
is
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Vector Algebra
Let the volume of a parallelopiped whose coterminous edges are given by
Let and be three unit vectors such that
Let be three vectors mutually perpendicular to each other and have same magnitude. If a vector
The angle between the straight lines, whose direction cosines are given by the equations
If the projection of the vector on the sum of the two vectors