firstly,
Find the projection of the vector
If
and
are two collinear vectors, then which of the following are incorrect: A.
, for some scalar
B.
C. the respective components of
and
are proportional D. both the vectors
and
have same direction, but different magnitudes
we know,
In triangle ABC (Fig 10.18) which of the following is not true:
Firstly let us consider,
Show that the points A, B and C with position vectors,
,
and
,respectively form the vertices of a right angled triangle.
We know Given position vectors of points A, B, and C are: Hence, proved that the given points form the vertices of a right angled triangle.
Find the position vector of the mid point of the vector joining the points P
and Q
.
The position vector of mid-point R of the vector joining points P \[(2,3,4)\] and Q \[(4,1,-2)\] is given by,
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are
and
respectively, in the ratio
We know that The position vector of point R dividing the line segment joining two points P and Q in the ratio m: n is given by:
Show that the vector
is equally inclined to the axes OX, OY, and OZ.
Firstly,
Find the direction cosines of the vector joining the points A
and B
directed from A to B.
We know that the Given points are A \[(1,2,-3)\] and B \[(-1,-2,1)\]. Now,
Find the direction cosines of the vector
Firstly,
Show that the vectors
and
are collinear.
Therefore, we can say that the given vectors are collinear.
Find a vector in the direction of vector
which has magnitude
units.
Firstly,
For given vectors,
and
, find the unit vector in the direction of the vector
We know that,
Find the unit vector in the direction of vector , where P and Q are the points
and
, respectively
We know that,
Find the unit vector in the direction of the vector
We know that
Find the sum of the vectors
Let us find the sum of the vectors:
Find the scalar and vector components of the vector with initial point
and terminal point
.
The scalar and vector components are: The vector with initial point P \[(2,1)\] and terminal point Q \[(-5,7)\] can be shown as, \[-7\widehat{i}\] and \[6\widehat{j}\] Thus, the required scalar...
Find the values of x and y so that the vectors
and
are equal
Given vectors \[2\widehat{i}+3\widehat{j}\] and \[x\widehat{i}+y\widehat{j}\] will be equal only if their corresponding components are equal. Thus, the required values of x and y are \[2\] and \[3\]...
Write two different vectors having same direction.
Two different vectors having same directions are: Let us
Write two different vectors having same magnitude
Compute the magnitude of the following vectors:
Given vectors are: