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Magnetic Field Due to Finite Wire

Which of the ...

Question

Which of the following quantities are always zero in SHM?

A

\to F \times \to a

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B

\to v \times \to r

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C

\to a \times \to r

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D

\to F \times \to r

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Solution

The correct options are
A $\to F \times \to a$
B $\to v \times \to r$
C $\to a \times \to r$
D $\to F \times \to r$
In SHM $\to F$ , $\to r$ , $\to v$ and $\to a$ are always along the same straight line either in the same direction or in opposite directions, so the angle between any of the pairs is either $0^{\circ}$ or $180^{\circ}$ and $sin 0^{\circ} = sin 180^{\circ} = 0$ . So cross product of any of the pair will also be equal to zero. Hence all options are correct.

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Similar questions

\to a, \to b, \to c

are three non-coplanar non-zero vectors and

\to r

is any vector, then

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b) =

Q. Assertion :If

\to r \times \to a = \to b, \to r . \to a = 1,

\to r = \to a + \to a \times \to b .

Reason: The solution of the

\to r \times \to a = \to b

\to r = \to a \times \to b

.

\to a, \to b, \to c

are three noncoplanar nonzero vectors and

\to r

is any vector in space then

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)

\to r \times \to a = \to b \times \to a; \to r \times \to b = \to a \times \to b; \to a \neq 0, \to b \neq 0, \to a \neq λ \to b; \to a

is not perpendicular to

\to b

\to r =

\to a = \to i + \to j

\to b = 2 \to j - \to k

\to r \times \to a = \to b \times \to a

\to r \times \to b = \to a \times \to b

\frac{\to r}{| \to r |}

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