Question

Show that:
$open vertical bar straight A with rightwards arrow on top plus straight B with rightwards arrow on top close vertical bar less-than or slanted equal to open vertical bar straight A with rightwards arrow on top close vertical bar space plus space open vertical bar straight B with rightwards arrow on top close vertical bar greater-than or slanted equal to space open vertical bar open vertical bar straight A with rightwards arrow on top close vertical bar minus open vertical bar straight B with rightwards arrow on top close vertical bar close vertical bar$

Solution

To show:
$open vertical bar straight A with rightwards arrow on top plus straight B with rightwards arrow on top close vertical bar space equals square root of straight A squared plus straight B squared plus 2 ABcosθ end root$

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$open vertical bar straight A with rightwards harpoon with barb upwards on top plus straight B with rightwards harpoon with barb upwards on top close vertical bar space less-than or slanted equal to space square root of straight A squared plus straight B squared plus 2 AB end root space space space space space space space space space space space space space space equals space square root of left parenthesis straight A plus straight B right parenthesis squared end root space space space space space space space space space space space space space space equals space straight A space plus space straight B Therefore comma space open vertical bar straight A with rightwards harpoon with barb upwards on top space plus space straight B with rightwards harpoon with barb upwards on top close vertical bar less-than or slanted equal to open vertical bar straight A with rightwards harpoon with barb upwards on top space close vertical bar space plus space open vertical bar space straight B with rightwards harpoon with barb upwards on top close vertical bar space Now comma space open vertical bar straight A with rightwards harpoon with barb upwards on top space plus space straight B with rightwards harpoon with barb upwards on top close vertical bar space equals space square root of straight A squared plus straight B squared plus 2 ABcosθ end root Since comma space cos space straight theta space greater-than or slanted equal to space minus space 1 therefore space open vertical bar straight A with rightwards harpoon with barb upwards on top space plus space straight B with rightwards harpoon with barb upwards on top close vertical bar greater-than or slanted equal to space square root of straight A squared plus straight B squared minus 2 AB end root space space space space space space space space space space space space space space space space space space space space equals square root of left parenthesis straight A minus straight B right parenthesis squared end root space space space space space space space space space space space space space space space space space space space equals open vertical bar straight A with rightwards harpoon with barb upwards on top space minus space straight B with rightwards harpoon with barb upwards on top close vertical bar space space space space space space space space space space space space space space space space space space space space equals space open vertical bar 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 vertical bar$
Hence proved.

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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

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.

What is module of vector?

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