If
Let
and
be two unit vectors and
is the angle between them. Then
is a unit vector if (A)
(B)
(C)
(D)
Here the correct answer is option d
If
is the angle between two vectors
and
, Then
only when (A)
(B)
(C)
(D)
Prove that
, if and only if
,
are perpendicular, given
.
It is given that Hence proved.
If
,
,
. are mutually perpendicular vectors of equal magnitudes, show that the vector
is equally inclined to
,
and
.
let us assume,
The scalar product of the vector
with a unit vector along the sum of vectors
and
is equal to one. Find the value of
.
Let us consider
Let
,
and
. Find a vector
which is perpendicular to both
and
, and
Assume,
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are
,
,
.
Firstly, Let’s assume a vector to be equally inclined to axes OX, OY, and OZ at angle \[\alpha \]. Then, the direction cosines of the vector are \[\cos \alpha \],\[\cos \alpha \]and \[\cos \alpha...
The two adjacent sides of a parallelogram are
and
. Find the unit vector parallel to its diagonal. Also, find its area.
we know that,
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are
and
externally in the ratio
. Also, show that P is the midpoint of the line segment RQ.
we know that,
Show that the points A
, B
and C
are collinear, and find the ratio in which B divides AC.
Let us consider
If
,
and
find a unit vector parallel to the vector
.
Let us consider
Find a vector of magnitude 5 units, and parallel to the resultant of the vectors
and
let us consider,
Find the value of x for which
is a unit vector.
we know ,
If
, then is it true that
? Justify your answer.
It is given that,
A girl walks
km towards west, then she walks
km in a direction
east of north and stops. Determine the girl’s displacement from her initial point of departure.
It is given that, Let O and B be the initial and final positions of the girl respectively. Then, the girl’s position can be shown as:
. Find the scalar components and magnitude of the vector joining the points P
and Q
.
let us consider,
Write down a unit vector in XY-plane, making an angle of
with the positive direction of x-axis.
let us consider,