हिंदी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान कक्षा ११

Can You Add Two Vectors Representing Physical Quantities Having Different Dimensions? Can You Multiply Two Vectors Representing Physical Quantities Having Different Dimensions?

Advertisements
Advertisements

प्रश्न

Can you add two vectors representing physical quantities having different dimensions? Can you multiply two vectors representing physical quantities having different dimensions?

संक्षेप में उत्तर
Advertisements

उत्तर

No, we cannot add two vectors representing physical quantities of different dimensions. However, we can multiply two vectors representing physical quantities with different dimensions.
Example: Torque,

\[\vec{\tau} = \vec{r} \times \vec{F}\]
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Physics and Mathematics - Short Answers [पृष्ठ २८]

APPEARS IN

एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
अध्याय 2 Physics and Mathematics
Short Answers | Q 7 | पृष्ठ २८

संबंधित प्रश्न

“It is more important to have beauty in the equations of physics than to have them agree with experiments”. The great British physicist P. A. M. Dirac held this view. Criticize this statement. Look out for some equations and results in this book which strike you as beautiful.


What are the dimensions of volume of a cube of edge a.


It is desirable that the standards of units be easily available, invariable, indestructible and easily reproducible. If we use foot of a person as a standard unit of length, which of the above features are present and which are not?


Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is, `[ x ] = M^a L^b T^c`.  The quantity mass


\[\int\frac{dx}{\sqrt{2ax - x^2}} = a^n \sin^{- 1} \left[ \frac{x}{a} - 1 \right]\] 
The value of n is


Find the dimensions of frequency .


Find the dimensions of Planck's constant h from the equation E = hv where E is the energy and v is the frequency.


Let I = current through a conductor, R = its resistance and V = potential difference across its ends. According to Ohm's law, product of two of these quantities equals the third. Obtain Ohm's law from dimensional analysis. Dimensional formulae for R and V are \[{\text{ML}}^2 \text{I}^{- 2} \text{T}^{- 3}\] and \[{\text{ML}}^2 \text{T}^{- 3} \text{I}^{- 1}\] respectively.


Test if the following equation is dimensionally correct:
\[h = \frac{2S cos\theta}{\text{ prg }},\]
where h = height, S = surface tension, ρ = density, I = moment of interia.


Is a vector necessarily changed if it is rotated through an angle?


Is it possible to add two vectors of unequal magnitudes and get zero? Is it possible to add three vectors of equal magnitudes and get zero?


Let ε1 and ε2 be the angles made by  \[\vec{A}\] and -\[\vec{A}\] with the positive X-axis. Show that tan ε1 = tan ε2. Thus, giving tan ε does not uniquely determine the direction of \[\vec{A}\].

  

Which of the sets given below may represent the magnitudes of three vectors adding to zero?


A vector \[\vec{A}\] points vertically upward and \[\vec{B}\] points towards the north. The vector product \[\vec{A} \times \vec{B}\] is


A situation may be described by using different sets coordinate axes having different orientation. Which the following do not depended on the orientation of the axis?
(a) the value of a scalar
(b) component of a vector
(c) a vector
(d) the magnitude of a vector.


Let the angle between two nonzero vectors \[\vec{A}\] and \[\vec{B}\] be 120° and its resultant be \[\vec{C}\].


If \[\vec{A} , \vec{B} , \vec{C}\] are mutually perpendicular, show that  \[\vec{C} \times \left( \vec{A} \times \vec{B} \right) = 0\] Is the converse true?


In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 s. If the speed of sound in water is 1460 ms-1. What is the distance of an enemy submarine? 


High speed moving particles are studied under


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×