Advertisements
Advertisements
प्रश्न
Let \[\vec{C} = \vec{A} + \vec{B}\]
पर्याय
\[\left| \vec{C} \right|\] is always greater than \[\left| \vec{A} \right|\]
It is possible to have \[\left| \vec{C} \right|\] < \[\left| \vec{A} \right|\] and \[\left| \vec{C} \right|\] < \[\left| \vec{B} \right|\]
C is always equal to A + B
C is never equal to A + B.
उत्तर
It is possible to have \[\left| \vec{C} \right|\] < \[\left| \vec{A} \right|\] and \[\left| \vec{C} \right|\] < \[\left| \vec{B} \right|\]
Statements (a), (c) and (d) are incorrect.
Given: \[\vec{C} = \vec{A} + \vec{B}\]
Here, the magnitude of the resultant vector may or may not be equal to or less than the magnitudes of \[\vec{A}\] and \[\vec{B}\] or the sum of the magnitudes of both the vectors if the two vectors are in opposite directions.
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”?
What are the dimensions of the ratio of the volume of a cube of edge a to the volume of a sphere of radius a?
Suggest a way to measure the thickness of a sheet of paper.
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 magnetic field B.
The relevant equation 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.
Can you add three unit vectors to get a unit vector? Does your answer change if two unit vectors are along the coordinate axes?
If \[\vec{A} \times \vec{B} = 0\] can you say that
(a) \[\vec{A} = \vec{B} ,\]
(b) \[\vec{A} \neq \vec{B}\] ?
Let \[\vec{A} = 5 \vec{i} - 4 \vec{j} \text { and } \vec{B} = - 7 \cdot 5 \vec{i} + 6 \vec{j}\]. Do we have \[\vec{B} = k \vec{A}\] ? Can we say \[\frac{\vec{B}}{\vec{A}}\] = k ?
Which of the sets given below may represent the magnitudes of three vectors adding to zero?
The resultant of \[\vec{A} \text { and } \vec{B}\] makes an angle α with \[\vec{A}\] and β with \[\vec{B}\],
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.
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.
Prove that \[\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0\].
If \[\vec{A} , \vec{B} , \vec{C}\] are mutually perpendicular, show that \[\vec{C} \times \left( \vec{A} \times \vec{B} \right) = 0\] Is the converse true?
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.
Round the following numbers to 2 significant digits.
(a) 3472, (b) 84.16. (c)2.55 and (d) 28.5
In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 s. If the speed of sound in water is 1460 ms-1. What is the distance of an enemy submarine?
If π = 3.14, then the value of π2 is ______