Question

Show that:

Solution

We have the inequality,
$negative 1 less-than or slanted equal to cosθ less-than or slanted equal to 1$
i.e., $negative 1 space less-than or slanted equal to space minus cos space straight theta space less-than or slanted equal to space 1 space$

Now, multiplying the inequality by 2AB,
$negative 2 A B space less-than or slanted equal to space minus 2 A B space cos theta space less-than or slanted equal to space 2 A B space$
Now adding A² + B², we get
$straight A squared space plus space straight B squared space minus space 2 AB space less-than or slanted equal to space straight A squared plus space straight B squared space minus space 2 ABcosθ space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space less-than or slanted equal to space straight A squared plus space straight B squared space plus space 2 AB open parentheses open vertical bar open vertical bar straight A with rightwards harpoon with barb upwards on top close vertical bar minus open vertical bar straight B with rightwards harpoon with barb upwards on top close vertical bar close vertical bar close parentheses squared space less-than or slanted equal to space open parentheses open vertical bar straight A with rightwards harpoon with barb upwards on top minus straight B with rightwards harpoon with barb upwards on top close vertical bar close parentheses squared space less-than or slanted equal to space open parentheses open vertical bar straight A with rightwards harpoon with barb upwards on top close vertical bar plus open vertical bar straight B with rightwards harpoon with barb upwards on top close vertical bar close parentheses squared space$
Taking square root, we get
$open vertical bar open vertical bar straight A with rightwards harpoon with barb upwards on top close vertical bar minus open vertical bar straight B with rightwards harpoon with barb upwards on top close vertical bar close vertical bar space less-than or slanted equal to space open vertical bar A with rightwards harpoon with barb upwards on top minus B with rightwards harpoon with barb upwards on top close vertical bar space less-than or slanted equal to space open vertical bar A with rightwards harpoon with barb upwards on top close vertical bar space plus space open vertical bar B with rightwards harpoon with barb upwards on top close vertical bar$
Hence, proved.

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Motion In A Plane

Show that:

Some More Questions From Motion in A Plane Chapter

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.

What is module of vector?

What are equal vectors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Motion In A Plane

Show that:

Some More Questions From Motion in A Plane Chapter

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.

What is module of vector?

What are equal vectors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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.