Advertisements
Advertisements
Question
Can a vector have zero component along a line and still have nonzero magnitude?
Solution
Yes, a vector can have zero components along a line and still have a nonzero magnitude.
Example: Consider a two dimensional vector \[2\hat { i } + 0 \hat {j}\]. This vector has zero components along a line lying along the Y-axis and a nonzero component along the X-axis. The magnitude of the vector is also nonzero.
Now, magnitude of \[2\hat { i} + 0 \hat {j}\] = \[\sqrt{2^2 + 0^2} = 2\]
APPEARS IN
RELATED QUESTIONS
“Every great physical theory starts as a heresy and ends as a dogma”. Give some examples from the history of science of the validity of this incisive remark
What are the dimensions of volume of a cube of edge a.
Suggest a way to measure the thickness of a sheet of paper.
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.
Find the dimensions of Planck's constant h from the equation E = hv where E is the energy and v is the frequency.
Find the dimensions of the coefficient of linear expansion α and
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.
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 it possible to add two vectors of unequal magnitudes and get zero? Is it possible to add three vectors of equal magnitudes and get zero?
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 component of a vector is
The radius of a circle is stated as 2.12 cm. Its area should be written as
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.
Let \[\vec{a} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j} + 5 \vec{k}\] Find the angle between them.
Prove that \[\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0\].
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.
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?
