Which of the following quantity/quantities are dependent on the choice of orientation of the co-ordinate axes?
$(a)$ $\vec{a}+\vec{b}$
$(b)$ $3 a_x+2 b_y$
$(c)$ $(\vec{a}+\vec{b}-\vec{c})$
Which of the following quantity/quantities are dependent on the choice of orientation of the co-ordinate axes?
$(a)$ $\vec{a}+\vec{b}$
$(b)$ $3 a_x+2 b_y$
$(c)$ $(\vec{a}+\vec{b}-\vec{c})$
- A
Only $(b)$
- B
Both $(a)$ and $(b)$
- C
Both $(a)$ and $(c)$
- D
Both $(b)$ and $(c)$
Similar Questions
Statement $I:$ If three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ are represented by three sides of a triangle and $\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}$, then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement $II:$ A triangle made up of three forces $\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}$ and $\overrightarrow{{F}}_{3}$ as its sides taken in the same order, satisfy the condition for translatory equilibrium.
In the light of the above statements, choose the most appropriate answer from the options given below:
Statement $I:$ If three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ are represented by three sides of a triangle and $\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}$, then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement $II:$ A triangle made up of three forces $\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}$ and $\overrightarrow{{F}}_{3}$ as its sides taken in the same order, satisfy the condition for translatory equilibrium.
In the light of the above statements, choose the most appropriate answer from the options given below:
- [JEE MAIN 2021]
$\overrightarrow{ A }=4 \hat{ i }+3 \hat{ j }$ and $\overrightarrow{ B }=4 \hat{ i }+2 \hat{ j }$. Find a vector parallel to $\overrightarrow{ A }$ but has magnitude five times that of $\vec{B}$.
$\overrightarrow{ A }=4 \hat{ i }+3 \hat{ j }$ and $\overrightarrow{ B }=4 \hat{ i }+2 \hat{ j }$. Find a vector parallel to $\overrightarrow{ A }$ but has magnitude five times that of $\vec{B}$.
The vectors $\vec{A}$ and $\vec{B}$ are such that
$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$
The angle between the two vectors is
The vectors $\vec{A}$ and $\vec{B}$ are such that
$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$
The angle between the two vectors is
- [AIIMS 2016]
Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are in the ratio $3:1.$ Which of the following relations is true
Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are in the ratio $3:1.$ Which of the following relations is true