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प्रश्न
A vector is not changed if
पर्याय
it is rotated through an arbitrary angle
it is multiplied by an arbitrary scalar
it is cross multiplied by a unit vector
it is slid parallel to itself.
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उत्तर
it is slid parallel to itself.
A vector is defined by its magnitude and direction. If we slide it to a parallel position to itself, then none of the given parameters, which define the vector, will change.
Let the magnitude of a displacement vector ( \[\vec{A}\] ) directed towards the north be 5 metres. If we slide it parallel to itself, then the direction and magnitude will not change.
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संबंधित प्रश्न
India has had a long and unbroken tradition of great scholarship — in mathematics, astronomy, linguistics, logic and ethics. Yet, in parallel with this, several superstitious and obscurantistic attitudes and practices flourished in our society and unfortunately continue even today — among many educated people too. How will you use your knowledge of science to develop strategies to counter these attitudes ?
What are the dimensions of volume of a cube of edge a.
What are the dimensions of volume of a sphere of radius a?
A unitless quantity
Find the dimensions of
(a) angular speed ω,
(b) angular acceleration α,
(c) torque τ and
(d) moment of interia I.
Some of the equations involving these quantities are \[\omega = \frac{\theta_2 - \theta_1}{t_2 - t_1}, \alpha = \frac{\omega_2 - \omega_1}{t_2 - t_1}, \tau = F . r \text{ and }I = m r^2\].
The symbols have standard meanings.
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.
The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = \[13 \cdot 6\] , Density of \[\text{ water} = {10}^3 kg/ m^3 , g = 9 \cdot 8 m/ s^2\] at Calcutta. Pressure
= hpg in usual symbols.
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.
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 a vector necessarily changed if it is rotated through an angle?
Can you add three unit vectors to get a unit vector? Does your answer change if two unit vectors are along the coordinate axes?
Can a vector have zero component along a line and still have nonzero magnitude?
Which of the sets given below may represent the magnitudes of three vectors adding to zero?
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 vector \[\vec{A}\] makes an angle of 20° and \[\vec{B}\] makes an angle of 110° with the X-axis. The magnitudes of these vectors are 3 m and 4 m respectively. Find the resultant.
Let \[\vec{a} = 4 \vec{i} + 3 \vec{j} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j}\]. Find the magnitudes of (a) \[\vec{a}\] , (b) \[\vec{b}\] ,(c) \[\vec{a} + \vec{b} \text { and }\] (d) \[\vec{a} - \vec{b}\].
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.
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 \[\vec{A} \times \vec{B}\].
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.
