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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

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.

To make best use of nubtrek, understand what is available.

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

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trek,

jogger,

exercise.

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» vector dot product of scalar multiple

→ `vec p cdot (lambda vec q) = lambda (vec p cdot vec q)`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

• Dot product with a scalar multiple of a vector equals the scalar multiple of the dot product with the 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 the vector dot product with the scalar multiple of a vector.

Starting on learning "Dot product of a scalar multiple". ;; In this page, you will learn about the vector dot product with the scalar multiple of a vector.

Given `vec p = 2i+j-k` and `lambda = 3.1` what is the scalar multiple `3.1 vec p`?

- `6.2i+3.1j-3.1k`
- `6.2i+j-k`

The answer is '`6.2i+3.1j-3.1k`'

Given the definition of dot product as

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

What is `vec p cdot (lambda vec q)`?

- `lambda(vec p cdot vec q)`
- `|p||lambda q|cos(theta)` if `lambda` is positive
- `lambda|p||q|cos(theta)`
- all the above

The answer is 'All the above'

Note that if `lambda` is a negative number, it equals `|p||lambda q|cos(180+theta)`.

Given the definition of dot product as

`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z`

What is `vec p cdot (lambda vec q)`?

- `lambda (vec p cdot vec q)`
- `p_x(lambda q_x)+p_y(lambda q_y)+p_z(lambda q_z)`
- `lambda (p_xq_x+p_yq_y+p_zq_z)`
- all the above

The answer is 'All the above'

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Dot Product of scalar multiple: ** For any vectors `vec p, vec q`

`vec p cdot (lambda vec q) = lambda (vec p cdot vec q)`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Given that `vec p cdot vec q = 3j+1.1k`, what is `vec p/(2.1) cdot vec q`?

- `3/(2.1)j+1.1/(2.1)k`
- `6.3j+2.31k`
- `3/(2.1)j+1.1k`

The answer is '`3/(2.1)j+1.1/(2.1)k`'.

*your progress details*

Progress

*About you*

Progress

Given vector p = 2i + j minus k and lambda = 3 point 1, what is the scalar multiple 3 point 1 multiplied vector p?

1

2

The answer is "6 point 2 i + 3 point 1 i minus 3 point 1 k"

Given the definition of dot product as vector p dot vector q = magnitude of vector p, magnitude of vector q, cos theta. What is vector p dot lambda times vector q?

1

2

3

4

The answer is "All the above". Note that if lambda is a negative number, it equals magnitude of p, magnitude of lambda q, cos 180 + theta.

Given the definition of dot product as vector p dot vector q = p x q x + p y q y + p z q z. What is vector p dot lambda times vector q?

1

2

3

4

The answer is 'All the above'

Dot product with a scalar multiple of a vector equals the scalar multiple of the dot product with the vector.

Dot Product of scalar multiple: For any vectors p and q ;; vector p dot, lambda times vector q =, lambda times, vector p dot vector q.

Given that vector p dot vector q = 3j + 1 point 1 k, what is vector p divided by 2 point 1, dot vector q?

1

2

3

The answer is "3 divided by 2.1 j + 1 point 1 divided by 2 point 1 k"