English
Karnataka Board PUCPUC Science Class 11

Which of the Sets Given Below May Represent the Magnitudes of Three Vectors Adding to Zero?

Advertisements
Advertisements

Question

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

Options

  • 2, 4, 8

  • 4, 8, 16

  •  1, 2, 1

  • 0.5, 1, 2

MCQ
Advertisements

Solution

1, 2, 1

1,2 and 1 may represent the magnitudes of three vectors adding to zero. For example one of the vector of length 1 should make an angle of  \[{135}^\circ\] with x axis and the other vector of length 1 makes an angle of \[{225}^\circ\]  with x axis. The third vector of length 2 should lie along x axis.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Physics and Mathematics - MCQ [Page 28]

APPEARS IN

HC Verma Concepts of Physics Volume 1 and 2 [English]
Chapter 2 Physics and Mathematics
MCQ | Q 2 | Page 28

RELATED QUESTIONS

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


If all the terms in an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?


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


A dimensionless quantity


Choose the correct statements(s):


Find the dimensions of the coefficient of linear expansion α and


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:
\[v = \sqrt{\frac{P}{\rho}},\]

where v = velocity, ρ = density, P = pressure


Test if the following equation is dimensionally correct:
\[V = \frac{\pi P r^4 t}{8 \eta l}\]

where v = frequency, P = pressure, η = coefficient of viscosity.


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 \[\vec{A} = 3 \vec{i} + 4 \vec{j}\]. Write a vector \[\vec{B}\] such that \[\vec{A} \neq \vec{B}\], but A = B.


Can you have  \[\vec{A} \times \vec{B} = \vec{A} \cdot \vec{B}\] with A ≠ 0 and B ≠ 0 ? What if one of the two vectors is zero?


The resultant of  \[\vec{A} \text { and } \vec{B}\] makes an angle α with  \[\vec{A}\] and β with \[\vec{B}\],


The component of a vector is 


Let \[\vec{C} = \vec{A} + \vec{B}\]


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


The magnitude of the vector product of two vectors \[\left| \vec{A} \right|\] and \[\left| \vec{B} \right|\] may be

(a) greater than AB
(b) equal to AB
(c) less than AB
(d) equal to zero.


A mosquito net over a 7 ft × 4 ft bed is 3 ft high. The net has a hole at one corner of the bed through which a mosquito enters the net. It flies and sits at the diagonally opposite upper corner of the net. (a) Find the magnitude of the displacement of the mosquito. (b) Taking the hole as the origin, the length of the bed as the X-axis, it width as the Y axis, and vertically up as the Z-axis, write the components of the displacement vector.


Let A1 A2 A3 A4 A5 A6 A1 be a regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact the resultant of these six vectors is zero, to prove that
cos 0 + cos π/3 + cos 2π/3 + cos 3π/3 + cos 4π/3 + cos 5π/3 = 0.
Use the known cosine values to verify the result.


Prove that \[\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0\].


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×