If , the do you think that A is necessarily equal to C? - Wired Faculty

Question

If $straight A with rightwards arrow on top cross times straight B with rightwards arrow on top space equals space straight C with rightwards arrow on top cross times straight B with rightwards arrow on top$ , the do you think that A is necessarily equal to C?

Solution

Here, $straight A with rightwards arrow on top cross times straight B with rightwards arrow on top space equals space straight C with rightwards arrow on top cross times straight B with rightwards arrow on top$
Let the angle between $straight A with rightwards arrow on top space and space straight B with rightwards arrow on top$ be $straight alpha$ and that between $straight B with rightwards arrow on top and space straight C with rightwards arrow on top$ be $straight beta$ .
∴ $AB space sinα space stack straight n subscript 1 with hat on top space equals space CB space sin space straight beta space stack straight n subscript 2 with hat on top$

$rightwards double arrow$ $space AB space sinα space equals space CB space sinβ$
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Therefore,
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$rightwards double arrow$ $straight A equals straight C sinβ over sinα$

Now, $space space if space straight alpha space equals space straight beta comma space space then space straight A space equals space straight C$
and $if space straight alpha not equal to straight beta comma$ then $straight A not equal to straight C$

Thus, A is not necessarily equal to C.

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Motion In A Plane

If $straight A with rightwards arrow on top cross times straight B with rightwards arrow on top space equals space straight C with rightwards arrow on top cross times straight B with rightwards arrow on top$ , the do you think that A is necessarily equal to C?

Some More Questions From Motion in A Plane Chapter

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Give one example of tensor.

Mock Test Series

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

If , the do you think that A is necessarily equal to C?

Some More Questions From Motion in A Plane Chapter

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Give one example of tensor.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If $straight A with rightwards arrow on top cross times straight B with rightwards arrow on top space equals space straight C with rightwards arrow on top cross times straight B with rightwards arrow on top$ , the do you think that A is necessarily equal to C?

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.