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✍️Revision Notes on Vectors✍️
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Some Basic Results of Vector Calculus:
1) Vectors in the same direction can be added by simply adding their magnitudes. But if the vectors to be added are in opposite directions, then their magnitudes are subtracted and not added.
2) Column vectors can be added by simply adding the values in each row.
3) You can find the magnitude of a vector in three dimensions by using the formula a2 = b2 + c2 + d2, where a is the magnitude of the vector, and b, c, and d are the components in each direction.
4) If l1a + m1b = l2a + m2b then l1 = l2 and m1 = m2
5) Collinear Vectors are also parallel vectors except that they lie on the same line.
6) When two vectors are parallel, the dot product of the vectors is 1 and their cross product is zero.
7)Two collinear vectors are always linearly dependent.
8) Two non-collinear non-zero vectors are always linearly independent
9) Three coplanar vectors are always linearly dependent.
10) Three non-coplanar non-zero vectors are always linearly independent
11) More than 3 vectors are always linearly dependent.
12) Three vectors are linearly dependent if they are coplanar that means any one of them can be represented as a linear combination of other two.
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Limited Seats Edition✍️Revision Notes on Vectors✍️
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Some Basic Results of Vector Calculus:
1) Vectors in the same direction can be added by simply adding their magnitudes. But if the vectors to be added are in opposite directions, then their magnitudes are subtracted and not added.
2) Column vectors can be added by simply adding the values in each row.
3) You can find the magnitude of a vector in three dimensions by using the formula a2 = b2 + c2 + d2, where a is the magnitude of the vector, and b, c, and d are the components in each direction.
4) If l1a + m1b = l2a + m2b then l1 = l2 and m1 = m2
5) Collinear Vectors are also parallel vectors except that they lie on the same line.
6) When two vectors are parallel, the dot product of the vectors is 1 and their cross product is zero.
7)Two collinear vectors are always linearly dependent.
8) Two non-collinear non-zero vectors are always linearly independent
9) Three coplanar vectors are always linearly dependent.
10) Three non-coplanar non-zero vectors are always linearly independent
11) More than 3 vectors are always linearly dependent.
12) Three vectors are linearly dependent if they are coplanar that means any one of them can be represented as a linear combination of other two.
STAY UNMUTED 🙂
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❗️❗️Electric Charges and Fields ❗️❗️
📌NCERT PICKS 📌
🔴 There is a spark or crackle when we take off oursynthetic clothes or sweater in dry whether.
🔴 It is observed that if two glass rods rubbed with wool or
silk cloth are brought close to each other, they repel each
other.
🔴 On rubbing two body, the mass of one body slightly get
lowered.
🔴 An ebonite rod held in hand can be charged by rubbing
with funnel but a copper rod cannot be charged like this.
🔴 When we touch a pith ball with an electrified plastic rod,
some of the negative charges on rod are transferred.
🔴 While calculating the force between the two charges
from coulomb's law, never take into account, the sign of
two charges. It just indicates nature of the force.
🔴 The test charge used to measure electric field at point is
taken as unit in magnitude or very small.
🔴 Field lines are always directed from higher potential to lower potential.
🔴 Neutral point is a point where resultant electric field is
zero.
🔴 When a charged particle enters with velocity at right
angle to the uniform field the trajectory is parabola.
🔴 A surface having same electric potential at every point is an equipotential surface.
🔴 Work done in moving a charge along an equipotential
surface is always zero.
🔴 Relative permitivity of the material is also known as
specific inductive capacitance.
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