A particle is moving with velocity 5 m/s towards east and its velocity changes to 5 m/s north in 10 seconds. Find the average acceleration in 10 seconds.
The vector \[\vec{P}=a\hat{i}+a\hat{j}+3\hat{k}\] and \[\vec{Q}=a\hat{i}-2\hat{j}-\hat{k}\] are perpendicular to each other. The positive value of a is
Two forces \[{{\vec{F}}_{1}}=10\hat{i}-\hat{j}-15\hat{k}\] and \[{{\vec{F}}_{2}}=10\hat{i}-\hat{j}-15\hat{k}\] act on a single point. The angle between \[{{\vec{F}}_{1}}\] and \[{{\vec{F}}_{2}}\] is nearly
The angle between two vector \[\overrightarrow{A}\And \overrightarrow{B}\] is \[\theta \]. vector \[\overrightarrow{R}\] is the resultant of vectors \[\overrightarrow{A}\And \overrightarrow{B},\] if \[\overrightarrow{R}\] makes an angle \[\frac{\theta }{2}\] with \[\overrightarrow{A}\] then
The unit vector parallel to the resultant of the vectors \[\overrightarrow{A}=4\hat{i}+3j+6\hat{k}\] and \[\overrightarrow{B}=-\hat{i}+3j-8\hat{k}\] is
The resultant of \[\vec{A}\] and \[\vec{B}\] is \[{{\vec{R}}_{1}}\]. On reversing the vector \[\vec{B},\] the resultant becomes \[{{\vec{R}}_{2}}\]. What is the value of \[R_{1}^{2}\,+\,R_{2}^{2}\,?\]
P, Q and R are three coplanar forces acting at a point and are in equilibrium. Given \[P=1.9318\,kg\,wt,\] \[sin{{\theta }_{1}}=0.9659,\] the value of R is (in kg wt)
The vectors from origin to the points A and B are \[\vec{A}=3\hat{i}\,-6\hat{j}\,+2\hat{k}\] and \[\vec{B}=2\hat{i}+\,\hat{j}\,-2\hat{k}\] respectively. The area of the triangle OAB be
If two vectors \[2\hat{i}\,+3\hat{j}\,+\,\hat{k}\] and \[-4\hat{i}\,-6\hat{j}\,-\lambda \hat{k}\] are parallel to each other, then value of \[\lambda \] is
The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at \[90{}^\circ \] with the force of smaller magnitude, what are the magnitudes of forces?
Given that X \[\vec{A}\,+\vec{B}+\vec{C}\]= 0, out of three vectors two are equal in magnitude and the magnitude of third vector is \[\sqrt{2}\] times that of either of two having equal magnitude. Then, angle between vectors are given by
\[\vec{A}-\vec{B}\] and \[\vec{A}\] are parallel. If \[|\vec{A}\times \vec{B}|\,=\,|\vec{A}.\vec{B}|,\] then angle between \[\vec{A}\] and \[\vec{B}\] will be
A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong?
A vector \[\vec{a}\] is turned without a change in its length through a small angle \[d\theta \]. The value of \[|\Delta \vec{a}|\] and \[\Delta a\] are respectively
If three vectors along coordinate axes represent the adjacent sides of a cube of length b, then the unit vector along its diagonal passing through the origin will be
If \[{{\bar{a}}_{1}}\] and \[{{\bar{a}}_{2}}\] are two non-collinear unit vectors and \[|{{\bar{a}}_{1}}+{{\bar{a}}_{2}}|=\sqrt{3},\] then the value of \[({{\bar{a}}_{1}}-{{\bar{a}}_{2}}).(2{{\bar{a}}_{1}}+{{\bar{a}}_{2}})\] is
