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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsVector AlgebraVector Addition

Parallelogram Law

In this page, the parallelogram law of vector addition is explained as a continuous addition of vectors.



click on the content to continue..

Note: Using Geometry, the triangle property of vector addition can be extended to explain parallelogram property of vector addition. In the coming pages, we establish a different point of view for the same.

Two taps simultaneously fill a bucket. One fills at `20` liter per hour and another fills at `10` liter per hour. What type of addition is this?

  • Sequential addition
  • Continuous addition
  • Continuous addition

Answer is 'continuous addition'. It is called continuous addition as the quantities are added continuously in small quantities over time. Scalar quantities can be added continuously..

A ball rolls with two velocity components `2`m/sec at `11^@`angle and `1.3`m/sec at `67^@` angle. vector addition parallelogram law The effective velocity of the ball is calculated using, which of the following?

  • Sequential addition of vectors
  • Continuous addition of vectors
  • Continuous addition of vectors
  • This does not look to be vector addition

answer is 'Continuous addition of vectors' The two vectors are acting together resulting in a vector sum.

A table is pulled by two persons with forces `f_a` and `f_b` with an angle `theta` between the two forces. vector addition example parallelogram The effective force on the table is calculated using in which of the following?

  • Sequential addition of vectors
  • Continuous addition of vectors
  • Continuous addition of vectors
  • This does not look to be vector addition

answer is 'Continuous addition of vectors' The two vectors are acting together resulting in a vector sum.

Continuous addition of two vectors is shown in the figure.
The magnitude of a vector is equivalently shown as length of the ray in a coordinate plane.parallelogram law of vector addition Let us see how to calculate `vec r`.

The vectors `vec x` and `vec y` can be split into components
 •  `vec x` = `vec a` + `vec b`
 •  `vec y` = `vec p` + `vec q`

parallelogram law of vector addition Note that `vec b` = `-vec q`
and `vec a` and `vec p` are in the same direction.

The component vectors are equivalently rearranged as shown in the figure.vector addition parallelogram law How will `vec a` and `vec p` interact?

  • Add in magnitude
  • Add in magnitude
  • Subtract in magnitude
  • cannot calculate

Answer is 'add in magnitude', as they are in the same direction

The component vectors are equivalently rearranged as shown in the figure.vector addition parallelogram law How will `vec b` and `vec q` interact?

  • cancel out to `0`
  • subtract in magnitude
  • subtract in magnitude
  • both the above

Answer is 'both the above', as they are in the opposite direction.

Note that the result forms a diagonal to the parallelogram.vector addition parallelogram law This is given as the parallelogram property of vector addition.

Two vectors form a parallelogram and the co-initial diagonal is the sum.

Parallelogram Property of vector addition parallelogram law of vector addition when two vectors are added, arrange such that their initial points coincide. In that configuration, complete a parallelogram with the two vectors as the two adjacent sides. The diagonal that starts from the initial point of the vectors is the sum of the two vectors.

                            
slide-show version coming soon