Advertisements
Advertisements
प्रश्न
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 \[\vec{A}\].
Advertisements
उत्तर
The direction of - \[\vec{A}\] is opposite to \[\vec{A}\].So, if vector \[\vec{A}\] and \[- \vec{A}\] make the angles ε1 and ε2 with the X-axis, respectively, then ε1 is equal to ε2 as shown in the figure:
Here, tan ε1 = tan ε2
Because these are alternate angles.
Thus, giving tan ε does not uniquely determine the direction of \[- \vec{A}\].
APPEARS IN
संबंधित प्रश्न
What are the dimensions of volume of a sphere of radius 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?
A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then
A unitless quantity
Choose the correct statements(s):
(a) All quantities may be represented dimensionally in terms of the base quantities.
(b) A base quantity cannot be represented dimensionally in terms of the rest of the base quantities.
(c) The dimensions of a base quantity in other base quantities is always zero.
(d) The dimension of a derived quantity is never zero in any base quantity.
Find the dimensions of linear momentum .
Find the dimensions of pressure.
Find the dimensions of Planck's constant h from the equation E = hv where E is the energy and v is the frequency.
Theory of relativity reveals that mass can be converted into energy. The energy E so obtained is proportional to certain powers of mass m and the speed c of light. Guess a relation among the quantities using the method of dimensions.
The component of a vector is
The radius of a circle is stated as 2.12 cm. Its area should be written as
Let \[\vec{C} = \vec{A} + \vec{B}\]
Let \[\vec{A} \text { and } \vec{B}\] be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angle 30° and 60° respectively, find the resultant.
Two vectors have magnitudes 2 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is (a) 1 unit, (b) 5 unit and (c) 7 unit.
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.
If \[\vec{A} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{B} = 4 \vec{i} + 3 \vec{j} + 2 \vec{k}\] find \[\vec{A} \times \vec{B}\].
Give an example for which \[\vec{A} \cdot \vec{B} = \vec{C} \cdot \vec{B} \text{ but } \vec{A} \neq \vec{C}\].
Draw a graph from the following data. Draw tangents at x = 2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve draw is y = 2x2 and the slope of tangent is \[\tan \theta = \frac{dy}{dx} = 4x\]
\[\begin{array}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200\end{array}\]
The electric current in a charging R−C circuit is given by i = i0 e−t/RC where i0, R and C are constant parameters of the circuit and t is time. Find the rate of change of current at (a) t = 0, (b) t = RC, (c) t = 10 RC.
If π = 3.14, then the value of π2 is ______
