firstly,
Find the projection of the vector \[\widehat{i}-\widehat{j}\] on the vector \[\widehat{i}+\widehat{j}\].
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Exercise 10.2
If \[\overrightarrow{a}\] and \[\overrightarrow{b}\] are two collinear vectors, then which of the following are incorrect: A. \[\overrightarrow{b}=\lambda \overrightarrow{a}\], for some scalar \[\lambda \] B. \[\overrightarrow{a}=\pm \overrightarrow{b}\] C. the respective components of \[\overrightarrow{a}\] and \[\overrightarrow{b}\] are proportional D. both the vectors \[\overrightarrow{a}\] and \[\overrightarrow{b}\] 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, \[\overrightarrow{a}=3\widehat{i}-4\widehat{j}-4\widehat{k}\] , \[\overrightarrow{b}=2\widehat{i}-\widehat{j}+\widehat{k}\] and \[\overrightarrow{c}=\widehat{i}-3\widehat{j}-5\widehat{k}\] ,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 \[(2,3,4)\] and Q \[(4,1,-2)\].
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 \[\widehat{i}+2\widehat{j}-\widehat{k}\] and \[-\widehat{i}+\widehat{j}+\widehat{k}\] respectively, in the ratio \[2:1\]
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 \[\widehat{i}+\widehat{j}+\widehat{k}\] is equally inclined to the axes OX, OY, and OZ.
Firstly,
Find the direction cosines of the vector joining the points A \[(1,2,-3)\] and B \[(-1,-2,1)\] 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 \[\widehat{i}+2\widehat{j}+3\widehat{k}\]
Firstly,
Show that the vectors \[2\widehat{i}-3\widehat{j}+4\widehat{k}\] and \[-4\widehat{i}+6\widehat{j}-8\widehat{k}\] are collinear.
Therefore, we can say that the given vectors are collinear.
Find a vector in the direction of vector \[5\widehat{i}-\widehat{j}+2\widehat{k}\] which has magnitude \[8\] units.
Firstly,
For given vectors, \[\overrightarrow{a}=2\widehat{i}-\widehat{j}+2\widehat{k}\] and \[\overrightarrow{b}=-\widehat{i}+\widehat{j}-\widehat{k}\], find the unit vector in the direction of the vector \[\overrightarrow{a}+\overrightarrow{b}\]
We know that,
Find the unit vector in the direction of vector , where P and Q are the points \[(1,2,3)\] and \[(4,5,6)\], respectively
We know that,
Find the unit vector in the direction of the vector \[\overrightarrow{a}=\widehat{i}+\widehat{j}+2\widehat{k}\]
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 \[(2,1)\] and terminal point \[(-5,7)\].
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 \[2\widehat{i}+3\widehat{j}\] and \[x\widehat{i}+y\widehat{j}\] 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: