The components of a vector a along the perpendicular to the non-zero vector b are respectively

The correct option is B a⃗·b⃗|b⃗| , |a⃗×b⃗||b⃗| The component of a along b =acosθ where θ is the angle between a and b H ...

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Standard XII

Physics

Centripetal Acceleration

The component...

Question

The components of a vector $\to a$ along the perpendicular to the non-zero vector $\to b$ are respectively

\frac{\to a \cdot \to b}{| \to a |}, \frac{| \to a \times \to b |}{| \to a |}

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\frac{\to a \cdot \to b}{| \to b |}, \frac{| \to a \times \to b |}{| \to b |}

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\frac{\to a \cdot \to b}{| \to a |}, \frac{| \to a . \to b |}{| \to a |}

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\frac{\to a \times \to b}{| \to a |}, \frac{| \to a \times \to b |}{| \to b |}

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Solution

The correct option is B $\frac{\to a \cdot \to b}{| \to b |}, \frac{| \to a \times \to b |}{| \to b |}$
The component of $\to a$ along $\to b$
$= a cos θ$ where $θ$ is the angle between $\to a$ and $\to b$
Hence $a cos θ$
$= \frac{\to a . \to b}{| b |}$ ... $(i)$

Similarly, the component of $\to a$ perpendicular to $\to b$
$= a sin θ$ where $θ$ is the angle between $\to a$ and $\to b$
Hence $a sin θ$
$= \frac{| \to a \times \to b |}{| b |}$

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Similar questions

Nonzero vectors $\to a, \to b, \to c$ satisfy $\to a . \to b$ =0, $(\to b - \to a) . (\to b + \to c)$ = 0 and 2 $| \to b + \to c | = | \to b - \to a |$ .

If = $\to a = μ \to b + 4 \to c$ then $μ$ = ______

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Q. If

\to a

and

\to b

are two vectors, such that

\to a \cdot \to b < 0

and

| \to a \cdot \to b | = | \to a \times \to b |

, then the angle between vectors

\to a

and

\to b

Q. If for three non-zero vectors

\to a, \to b

and

\to c, \to a \cdot \to b = \to a \cdot \to c

and

\to a \times \to b = \to a \times \to c

, then show that

\to b = \to c

Q. Find

| \to a - \to b |

, if two vectors

\to a

and

\to b

are such that

| \to a | = 2

| \to b | = 3

and

\to a . \to b = 4

If \to a

and

\to b

are vectors such that

| \to a \cdot \to b | = | \to a \times \to b |

and

\to a \cdot \to b < 0,

then the angle between

\to a

and

\to b

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The components of a vector →a along the perpendicular to the non-zero vector →b are respectively

The components of a vector $\to a$ along the perpendicular to the non-zero vector $\to b$ are respectively