What is the formula to calculate the magnitude of vector $$p = $$ ?

The magnitude is calculated as $$||p|| = \text{sqrt}(3^2 + (-9)^2) = 9.5$$ .

How do you find the direction angle of a vector with initial side at (0, 0) and terminal side at B?

Use the formula $$\theta = \tan^{-1}(\frac{y}{x})$$ , where B = (x, y). For B = (-5, 6), the angle is approximately 129.81 degrees.

What is the difference between a vector and a scalar?

A vector has both magnitude and direction, while a scalar has only magnitude.

What is the unit vector in the direction of vector $$v = $$ ?

The unit vector is $$\frac{v}{||v||} = $$ .

How do you add two vectors graphically?

To add two vectors graphically, place the tail of the second vector at the head of the first vector and draw the resultant vector from the tail of the first to the head of the second.

What is the dot product of two vectors?

The dot product of vectors $$a = $$ and $$b = $$ is calculated as $$a ullet b = a_1b_1 + a_2b_2$$ .

What is the cross product of two vectors?

The cross product of vectors $$a = $$ and $$b = $$ results in a vector that is perpendicular to both $$a$$ and $$b$$ , calculated as $$a \times b = $$ .

What is the significance of the angle between two vectors?

The angle between two vectors affects their dot product and can indicate whether they are orthogonal (90 degrees), parallel (0 or 180 degrees), or neither.

PreCalculus: Vectors Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a vector?

Back

A vector is a mathematical object that has both magnitude and direction, represented as an ordered pair or triplet of numbers in a coordinate system.

Tags

CCSS.HSN.VM.A.1

2.

FLASHCARD QUESTION

Front

What is a scalar?

Back

A scalar is a quantity that is fully described by a magnitude alone, without any direction.

Tags

CCSS.HSN.VM.A.1

3.

FLASHCARD QUESTION

Front

What is the magnitude of a vector?

Back

Tags

CCSS.HSN.VM.A.1

4.

FLASHCARD QUESTION

Front

Which of the following is always positive: vector, scalar, direction, or magnitude?

Back

Magnitude is always positive.

Tags

CCSS.HSN.VM.A.1

5.

FLASHCARD QUESTION

Front

How do you find the directional angle of a vector?

Back

Tags

CCSS.HSN.VM.A.1

6.

FLASHCARD QUESTION

Front

Back

The directional angle is approximately 71.6 degrees.

Tags

CCSS.HSN.VM.A.1

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.VM.A.1

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