Vector a lies in x - y plane- has magnitude of 18 units and points in a direction 250- from positive x-axis- Vector b has magnitude 12 units and points in positive z-axis- What is C - C - b -A- 10 rev - sB- 20 rev - sC- 30 rev - sD- 40 rev - s

The correct option is D 40 rev/s The angle between a⃗ and b⃗ is 90° as a⃗ is in x – y plane and b⃗ is along positive z. ∴ |a⃗| = |a⃗ × a⃗|= ab sin 90° ⇒ c ...

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Byju's Answer

Standard XII

Physics

Vector Component

Vector a lies...

Question

Vector $\to a$ lies in x – y plane, has magnitude of 18 units and points in a direction 250° from positive x-axis. Vector $\to b$ has magnitude 12 units and points in positive z-axis.
What is $\to c = \to c \times \to b$ ?

10 rev/s

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20 rev/s

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30 rev/s

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40 rev/s

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Solution

The correct option is D
40 rev/s

The angle between $\to a$ and $\to b$ is 90° as $\to a$ is in x – y plane and $\to b$ is along positive z.

∴ $| \to a |$ = $| \to a \times \to a |$ = ab sin 90°

⇒ c = ab = 18 units

Also, the direction of $\to c$ is perpendicular to $\to b$ as well as $\to a$ , and using the screw rule we can see that it points 160° from positive x-axis, making it 90° from $\to a$ , and from $\to b$ in the x – y plane.

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Vector →a lies in x – y plane, has magnitude of 18 units and points in a direction 250° from positive x-axis. Vector →b has magnitude 12 units and points in positive z-axis. What is →c=→c × →b?

Vector $\to a$ lies in x – y plane, has magnitude of 18 units and points in a direction 250° from positive x-axis. Vector $\to b$ has magnitude 12 units and points in positive z-axis.
What is $\to c = \to c \times \to b$ ?