Which of the following is independent of the choice of co-ordinate system
$\vec P + \vec Q + \vec R$
$({P_x} + {Q_x} + {R_x})\hat i$
${P_x}\hat i + {Q_y}\hat j + {R_z}\hat k$
None of these
Given that $\vec A\, + \,\vec B\, = \,\vec C\,.$ If $\left| {\vec A} \right|\, = \,4,\,\,\left| {\vec B} \right|\, = \,5\,\,$ and $\left| {\vec C} \right|\, =\,\sqrt {61}$ the angle between $\vec A\,\,$ and $\vec B$ is ....... $^o$
The magnitude of a given vector with end points $ (4, -4, 0)$ and $(-2, -2, 0)$ must be
Assertion $A$ : If $A, B, C, D$ are four points on a semi-circular arc with centre at $'O'$ such that $|\overrightarrow{{AB}}|=|\overrightarrow{{BC}}|=|\overrightarrow{{CD}}|$, then $\overrightarrow{{AB}}+\overrightarrow{{AC}}+\overrightarrow{{AD}}=4 \overrightarrow{{AO}}+\overrightarrow{{OB}}+\overrightarrow{{OC}}$
Reason $R$ : Polygon law of vector addition yields $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{A D}=2 \overrightarrow{A O}$
In the light of the above statements, choose the most appropriate answer from the options given below
A particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (Assuming particle is initially at rest)
${\vec F_1} = 5\hat i - 5\hat j + 5\hat k$ ${\vec F_2} = 2\hat i + 8\hat j + 6\hat k$
${\vec F_3} = - 6\hat i + 4\hat j - 7\hat k$ ${\vec F_4} = - \hat i - 3\hat j - 2\hat k$
Then the particle will move
The value of the sum of two vectors $\overrightarrow A $ and $\overrightarrow B $ with $\theta $ as the angle between them is