Advertisements
Advertisements
प्रश्न
Let \[\vec{A} = 3 \vec{i} + 4 \vec{j}\]. Write a vector \[\vec{B}\] such that \[\vec{A} \neq \vec{B}\], but A = B.
Advertisements
उत्तर
A vector \[\vec{B}\] such that \[\vec{A} \neq \vec{B}\], but A = B are as follows:
\[(i) \ \vec{ B} = 3 \vec{i} - 4 \vec{j} \]
\[(ii) \ \vec{ B} = 3 \vec{j} + 4 \vec{k} \]
\[(iii) \ \vec{ B} = 3 \vec{k} + 4 \vec{i} \]
\[(iv) \ \vec{ B} = 3 \vec{j} - 4 \vec{k}\]
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.
What are the dimensions of volume of a cube of edge a.
If all the terms in an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?
It is desirable that the standards of units be easily available, invariable, indestructible and easily reproducible. If we use foot of a person as a standard unit of length, which of the above features are present and which are not?
A unitless quantity
Find the dimensions of magnetic permeability \[\mu_0\]
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 the coefficient of linear expansion α and
Test if the following equation is dimensionally correct:
\[v = \sqrt{\frac{P}{\rho}},\]
where v = velocity, ρ = density, P = pressure
Can you add three unit vectors to get a unit vector? Does your answer change if two unit vectors are along the coordinate axes?
Let ε1 and ε2 be the angles made by \[\vec{A}\] and -\[\vec{A}\] with the positive X-axis. Show that tan ε1 = tan ε2. Thus, giving tan ε does not uniquely determine the direction of \[\vec{A}\].
If \[\vec{A} \times \vec{B} = 0\] can you say that
(a) \[\vec{A} = \vec{B} ,\]
(b) \[\vec{A} \neq \vec{B}\] ?
The resultant of \[\vec{A} \text { and } \vec{B}\] makes an angle α with \[\vec{A}\] and β with \[\vec{B}\],
The component of a vector is
The radius of a circle is stated as 2.12 cm. Its area should be written as
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.
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 \[\vec{A} \times \vec{B}\].
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?
Give an example for which \[\vec{A} \cdot \vec{B} = \vec{C} \cdot \vec{B} \text{ but } \vec{A} \neq \vec{C}\].
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 \[\tan \theta = \frac{dy}{dx} = 4x\]
\[\begin{array}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200\end{array}\]
Round the following numbers to 2 significant digits.
(a) 3472, (b) 84.16. (c)2.55 and (d) 28.5
