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
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 ?
A dimensionless quantity
Find the dimensions of linear momentum .
Find the dimensions of pressure.
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.
Is a vector necessarily changed if it is rotated through an angle?
If \[\vec{A} \times \vec{B} = 0\] can you say that
(a) \[\vec{A} = \vec{B} ,\]
(b) \[\vec{A} \neq \vec{B}\] ?
A vector is not changed if
The component of a vector is
Let \[\vec{C} = \vec{A} + \vec{B}\]
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.
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) \[\vec{a} - \vec{b}\].
Refer to figure (2 − E1). Find (a) the magnitude, (b) x and y component and (c) the angle with the X-axis of the resultant of \[\overrightarrow{OA}, \overrightarrow{BC} \text { and } \overrightarrow{DE}\].

Suppose \[\vec{a}\] is a vector of magnitude 4.5 units due north. What is the vector (a) \[3 \vec{a}\], (b) \[- 4 \vec{a}\] ?
Let A1 A2 A3 A4 A5 A6 A1 be a regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact the resultant of these six vectors is zero, to prove that
cos 0 + cos π/3 + cos 2π/3 + cos 3π/3 + cos 4π/3 + cos 5π/3 = 0.
Use the known cosine values to verify the result.

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?
A curve is represented by y = sin x. If x is changed from \[\frac{\pi}{3}\text{ to }\frac{\pi}{3} + \frac{\pi}{100}\] , find approximately the change in y.
