Question
Give an example for which $\overrightarrow{\text{A}}.\overrightarrow{\text{B}}=\overrightarrow{\text{C}}.\overrightarrow{\text{B}}$ but $\overrightarrow{\text{A}}\neq\overrightarrow{\text{C}}.$
✓
Answer
For example, as shown in the figure,
$\overrightarrow{\text{A}}\perp\overrightarrow{\text{B}}:\overrightarrow{\text{B}} \ \text{along west}$
$\overrightarrow{\text{B}}\perp\overrightarrow{\text{C}}:\overrightarrow{\text{A}}\text{ along south}$
$\overrightarrow{\text{C}} \text{along north}$
$\overrightarrow{\text{A}}.\overrightarrow{\text{B}}=0$ $\therefore\overrightarrow{\text{A}}.\overrightarrow{\text{B}}=\overrightarrow{\text{B}}.\overrightarrow{\text{C}}$
$\overrightarrow{\text{B}}.\overrightarrow{\text{C}}=0$ But $\overrightarrow{\text{B}}\neq\overrightarrow{\text{C}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin.
Give any two examples to explain Newton's third law.
If the value of universal gravitational constant in SI is $6.6 \times 10^{-11} Nm ^2 kg^{-2}$, then find its value in CGS system.
→A small spherical ball of radius r falls with velocity v through a liquid having coefficient of viscosity $\eta$. Find the viscous drag F on the ball assuming it depends on $\eta, r$ and v . Take $K =6 \pi$.
→A proton beam is going from east to west. Is there an electric current? If yes, in what direction?
When 100 atm pressure is applied on a sphere in the normal and uniform direction its volume decreases by 0.01%. Calculate the Bulk's Modulus of elasticity of this material.
Calculate the work done in blowing a soap bubble from a radius of 2cm to 3cm. The surface tension of the soap solution is 30 dynes cm.
The photograph of a house occupies an area of $1.75 cm^2$ on a 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 $m ^2$. What is the linear magnification of the projectorscreen arrangement.
→The density of atmosphere is 1.29kg m-3 at sea level, where atmospheric pressure is 1.013 × 105 Pa. If we assume that atmospheric density does not change with altitude, then what should be the height of the atmosphere?
Prove that when there is an angle $\frac{2}{3} \pi$ between two vectors of equal magnitude, then the magnitude of resultant vector will be equal to the magnitude of one of the vectors.
→