Advertisements
Advertisements
प्रश्न
The resultant of \[\vec{A} \text { and } \vec{B}\] makes an angle α with \[\vec{A}\] and β with \[\vec{B}\],
पर्याय
α < β
α < β if A < B
α < β if A > B
α < β if A = B
Advertisements
उत्तर
α < β if A > B
The resultant of two vectors is closer to the vector with the greater magnitude.
Thus, α < β if A > B
APPEARS IN
संबंधित प्रश्न
Some of the most profound statements on the nature of science have come from Albert Einstein, one of the greatest scientists of all time. What do you think did Einstein mean when he said : “The most incomprehensible thing about the world is that it is comprehensible”?
If two quantities have same dimensions, do they represent same physical content?
Suggest a way to measure the thickness of a sheet of paper.
The dimensions ML−1 T−2 may correspond to
Find the dimensions of linear momentum .
Find the dimensions of pressure.
Find the dimensions of electric field E.
The relevant equations are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]
where F is force, q is charge, v is speed, I is current, and a is distance.
Find the dimensions of the specific heat capacity c.
(a) the specific heat capacity c,
(b) the coefficient of linear expansion α and
(c) the gas constant R.
Some of the equations involving these quantities are \[Q = mc\left( T_2 - T_1 \right), l_t = l_0 \left[ 1 + \alpha\left( T_2 - T_1 \right) \right]\] and PV = nRT.
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.
Test if the following equation is dimensionally correct:
\[v = \sqrt{\frac{P}{\rho}},\]
where v = velocity, ρ = density, P = pressure
Let x and a stand for distance. Is
\[\int\frac{dx}{\sqrt{a^2 - x^2}} = \frac{1}{a} \sin^{- 1} \frac{a}{x}\] dimensionally correct?
Is a vector necessarily changed if it is rotated through an angle?
Can a vector have zero component along a line and still have nonzero magnitude?
A vector \[\vec{A}\] points vertically upward and \[\vec{B}\] points towards the north. The vector product \[\vec{A} \times \vec{B}\] is
The component of a vector is
Suppose \[\vec{a}\] is a vector of magnitude 4.5 units due north. What is the vector (a) \[3 \vec{a}\], (b) \[- 4 \vec{a}\] ?
Two vectors have magnitudes 2 m and 3m. The angle between them is 60°. Find (a) the scalar product of the two vectors, (b) the magnitude of their vector product.
Give an example for which \[\vec{A} \cdot \vec{B} = \vec{C} \cdot \vec{B} \text{ but } \vec{A} \neq \vec{C}\].
Round the following numbers to 2 significant digits.
(a) 3472, (b) 84.16. (c)2.55 and (d) 28.5
