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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

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

Welcome to **nub****trek**.

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The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

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jogger,

exercise.

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Vector Dot Product: Projection form

» component in parallel is calculated by the angle

→ `vec p cdot vec q` ` = |vec p| |vec q| cos theta`

→ Note that `|vec a| = |vec q|cos theta`

→ `vec a` is the projection of `vec q` on `vec p`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

Vector dot product can be used to find **projection of a vector** on a line or on another vector.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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In this page, you will learn about computing projection of vector using vector dot product.

Starting on learning "vector dot product in the form, projection of a vector". ;; In this page, you will learn about computing projection of vector using vector dot product.

Vector dot product is understood as product between components in parallel to each other.

In finding the component in parallel to one vector the vector is projected on to another in the figure, What is `a` ?

- `a` is the projection of `vec q` onto `vec p`
- `a` is the projection of `vec p` onto `vec q`

The answer is '`a` is the projection of `vec q` onto `vec p`'

The vector dot product can be used to find projection of a vector on a line.

Consider the line given by `vec s` and the vector `vec p` as shown in the figure. We know that `vec s cdot vec p = |vec s| |vec p| cos theta`.

To find the projection of `vec p` on `vec s`, which of the following can be used?

- `hat s cdot vec p`, where `hat s` is unit vector
- `(vec s)/(|vec s|) cdot vec p`
- both the above

The answer is 'both the above'.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Projection of a vector: ** Projection of a vector `vec p` on a line in direction `vec s` is

`= vec p cdot hat s`

where `hat s` is the unit vector along `vec s`.

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Two vectors `vec p` and `vec q` with magnitudes `2` and `3` respectively are at an angle `60^@`. What is the projection of `vec p` on `vec q`?

- `2 xx cos 60^@`
- `2 xx 1/2`
- 1
- all the above

The answer is 'All the above'.

*your progress details*

Progress

*About you*

Progress

Vector dot product is understood as product between components in parallel to each other. In finding the component in parallel to one vector, the vector is projected on to another. In the figure what is a?

1

2

The answer is "a is the projection of vector q onto vector p"

The vector dot product can be used to find projection of a vector on a line.

Consider the line given by vector s and the vector p as shown in the figure. We know that vector s dot vector p = magnitude of vector s multiplied magnitude of vector p multiplied cos theta. ; To find the projection of vector p on vector s, which of the following can be used?

1

2

3

The answer is "both the above".

Vector dot product can be used to find projection of a vector on a line or on another vector.

Projection of a vector: Projection of a vector p on a line in direction vector s is ; vector p dot hat s ; where hat s is the unit vector along vector s.

Two vector p and q with magnitudes 2 and 3 respectively are at an angle 60 degree. What is the projection of vector p on vector q?

1

2

3

4

The answer is "all the above".