If the two directional cosines of a vectors are $$\dfrac { 1 }{ \sqrt { 2 } } $$ and $$\dfrac { 1 }{ \sqrt { 3} } $$ then the value of third directional cosines is
we have, $$\cos ^2\alpha +\cos ^2\beta +\cos ^2\gamma =1$$ $$\left ( \dfrac{1}{\sqrt{2}} \right )^2+\left ( \dfrac{1}{\sqrt{3}} \right )^2+\cos ^2\gamma =1$$ $$\cos ^2\gamma =1-\dfrac{1}{2}-\dfrac{1}{3}=\dfrac{1}{6}$$ $$\therefore \cos \gamma =\dfrac{1}{\sqrt{6}}$$
A body of mass $$5\ kg$$ starts from the origin with an initial velocity $$\vec{v}_0$$ = $$(30\hat{i} + 40\hat{j})m/s$$. If a constant force $$\vec{F} = -(\hat{i} + 5\hat{j})N$$ acts on the body, the time in which the Y-component of the velocity becomes zero is:
If vectors $$\vec{A} = \hat{i} + 2\hat{j} + 4\hat{k}$$ and $$\vec{B} = 5\hat{i}$$ represent the two sides of a triangle, then the third side of the triangle can have length equal to
Assertion(A): A vector is not changed if it is slid parallel to itself Reason(R): Two parallel vectors of same magnitude are said to be equal vectors
Of the vectors given below, the parallel vectors are $$\vec{A}=6\hat{i} +8\hat{j}$$ $$\vec{B}=210\hat{i}+280\hat{k}$$ $$\vec{C}=5.1\hat{i}+6.8\hat{j}$$ $$\vec{D}=3.6\hat{i}+8\hat{j}+48\hat{k}$$
Let two like parallel forces are acting, at points $$A$$ and $$B$$ such that the force at $$A$$ is double than the force at $$B$$. If $$C$$ is the point of action of the resultant, then $$AC/BC$$ is
Which of the following statement(s) is/are incorrect?
A body of mass $$5\ kg$$ starts from the origin with an initial velocity $$\vec{v}_0$$ = $$(30\hat{i} + 40\hat{j})m/s$$. If a constant force $$\vec{F} = -(\hat{i} + 5\hat{j})N$$ acts on the body, the time in which the Y-component of the velocity becomes zero is:
The sum and difference of two vectors are equal in magnitude: $$|\overrightarrow A + \overrightarrow B| = |\overrightarrow A - \overrightarrow B|$$. Prove that $$\overrightarrow A \bot \overrightarrow B.$$
Find 'm' if $$\vec{P}=\hat{i}-3\hat{j}+4\hat{k}$$ and $$\vec{Q}=m\hat{i}-6\hat{j}+8\hat{k}$$ have the same direction.
Arrange the vector addition so that their magnitude in increasing order are (a) Two vectors $$\vec { A }$$ and $$\vec { B }$$ are parallel (b) Two vectors$$\vec { A }$$ and $$\vec { B }$$ making an angle $$60 ^ { \circ }$$ (c) Two vectors$$\vec { A }$$ and $$\vec { B }$$ making an angle$$120 ^ { \circ }$$ (d) Two vectors$$\vec { A }$$ and $$\vec { B }$$ are antiparallel