Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
(b) equal to AB
(c) less than AB
(d) equal to zero.
The magnitude of the vector product of two vectors \[\left| \vec{A} \right|\] and \[\left| \vec{B} \right|\] may be less than or equal to AB, or equal to zero, but cannot be greater than AB.
APPEARS IN
संबंधित प्रश्न
“Politics is the art of the possible”. Similarly, “Science is the art of the soluble”. Explain this beautiful aphorism on the nature and practice of science.
“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.
Suggest a way to measure the thickness of a sheet of paper.
The dimensions ML−1 T−2 may correspond to
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 frequency .
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.
Can you add two vectors representing physical quantities having different dimensions? Can you multiply two vectors representing physical quantities having different dimensions?
Is the vector sum of the unit vectors \[\vec{i}\] and \[\vec{i}\] a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?
A vector \[\vec{A}\] points vertically upward and \[\vec{B}\] points towards the north. The vector product \[\vec{A} \times \vec{B}\] is
Let \[\vec{C} = \vec{A} + \vec{B}\]
Add vectors \[\vec{A} , \vec{B} \text { and } \vec{C}\] each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.
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 \[\tan \theta = \frac{dy}{dx} = 4x\]
\[\begin{array}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200\end{array}\]
A curve is represented by y = sin x. If x is changed from \[\frac{\pi}{3}\text{ to }\frac{\pi}{3} + \frac{\pi}{100}\] , find approximately the change in y.
The changes in a function y and the independent variable x are related as
\[\frac{dy}{dx} = x^2\] . Find y as a function of x.
Write the number of significant digits in (a) 1001, (b) 100.1, (c) 100.10, (d) 0.001001.
Round the following numbers to 2 significant digits.
(a) 3472, (b) 84.16. (c)2.55 and (d) 28.5
Jupiter is at a distance of 824.7 million km from the Earth. Its angular diameter is measured to be 35.72˝. Calculate the diameter of Jupiter.
