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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.

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### Parallelogram Law

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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?

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

• 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. The effective force on the table is calculated using in which of the following?

• 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. 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

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. How will vec a and vec p interact?

• 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. 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. 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 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