Vectors

Front

What is a vector?

Back

A vector is a quantity that has both magnitude and direction, represented graphically by an arrow.

Tags

CCSS.HSN.VM.A.1

Front

How do you add two vectors graphically?

Back

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

Tags

CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

Front

What is the Pythagorean Theorem used for in vector addition?

Back

The Pythagorean Theorem is used to find the magnitude of the resultant vector when two vectors are at right angles to each other.

Front

What is the formula for the resultant vector when combining two vectors at right angles?

Back

The resultant vector R can be calculated using R = √(A² + B²), where A and B are the magnitudes of the two vectors.

Tags

CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

Front

How do you find the angle of a resultant vector?

Back

The angle θ can be found using θ = tan⁻¹(opposite/adjacent) for right-angled vectors.

Tags

CCSS.HSN.VM.A.2

Front

What does the notation represent?

Back

The notation represents a vector in a two-dimensional space, where x is the horizontal component and y is the vertical component.

Tags

CCSS.HSN.VM.A.1

Front

How do you multiply a vector by a scalar?

Back

To multiply a vector by a scalar, multiply each component of the vector by the scalar.

Tags

CCSS.HSN-VM.B.5A

CCSS.HSN-VM.B.5B

Front

What is the result of adding the vectors <2, 3> and <4, -1>?

Back

The result is <6, 2>.

Tags

CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

Front

What is the difference between a scalar and a vector?

Back

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

Tags

CCSS.HSN.VM.A.1

Front

How do you subtract one vector from another?

Back

To subtract vector B from vector A, you add the opposite of vector B to vector A: A - B = A + (-B).

Tags

CCSS.HSN-VM.B.4C