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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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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

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learn.

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Vector Addition : Parallelogram Law

» **continuous addition** of `vec x` and `vec y`

→ `vec x = vec a + vec b`

→ `vec y = vec p + vec q`

→ the co-initial diagonal of the parallelogram formed by sides `vec x` and `vec y`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

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

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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

Starting on learning "Parallelogram Law of vector addition". ;; In this page, the parallelogram law of vector addition is explained as a continuous addition of vectors.

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

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. The effective velocity of the ball is calculated using...

- Sequential 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. The effective force on the table is calculated using ....

- Sequential 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. 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?

- 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. How will `vec b` and `vec q` interact?

- cancel out to `0`
- 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.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

** 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.

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

*your progress details*

Progress

*About you*

Progress

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

Sequential addition

continuous

Continuous addition

The 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 meter per sec in 11 degree angle and 1 point 3 meter per sec at 67 degree angle. The effective velocity of the ball is calculated using...

sequential

Sequential addition of vectors

continuous

Continuous addition of vectors

does;not;look

This does not look to be vector addition

The answer is "Continuous addition of vector". 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 ...

sequential

Sequential addition of vectors

continuous

Continuous addition of vectors

does;not;look

This does not look to be vector addition

The 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 vector r.

The vector x and vector y can be split into components ;; vector x = vector a + vector b ;; vector y = vector p + vector q ;; Note that vector b = minus vector q ;; and vector a and vector p are in the same direction.

The component vectors are equivalently rearranged as shown in the figure. ;; How will vector a and vector p interact?

add

Add in magnitude

subtract

Subtract in magnitude

cannot;not;calculate

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

cancel out to 0

subtract;magnitude

subtract in magnitude

both;above

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.