Understanding Vectors in Physics

What is a vector and how does it differ from a scalar?

• A vector has only magnitude; a scalar has both magnitude and direction.

• A vector has both magnitude and direction; a scalar has only magnitude.

• A vector is a single point in space; a scalar is a line.

• A vector can be represented as a number; a scalar cannot.

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CCSS.HSN.VM.A.1

Define the term 'resultant vector'.

• The resultant vector is the vector sum of two or more vectors.

• The resultant vector is the difference between two vectors.

• The resultant vector is the average of two vectors.

• The resultant vector is a scalar quantity derived from vectors.

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CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

How do you calculate the resultant vector of two vectors at an angle?

• R = A + B + θ

• R = A² - B² + 2ABtan(θ)

• R = A - B + 2ABsin(θ)

• R = √(A² + B² + 2ABcos(θ))

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CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

Explain the process of resolving a vector into its components.

• The components are calculated using Vx = V * tan(θ) and Vy = V * sec(θ).

• The components of a vector can be found using Vx = V * cos(θ) and Vy = V * sin(θ).

• The components of a vector are found by adding the magnitudes directly.

• Vectors cannot be resolved into components without a reference point.

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CCSS.HSN.VM.A.2

What are the two components of a vector when resolved at right angles?

• Tangential component and axial component

• Diagonal component and radial component

• Magnitude component and direction component

• Horizontal component and vertical component

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CCSS.HSN.VM.A.2

If a vector has a magnitude of 10 units and is directed at 30 degrees, what are its components?

• x: 7 units, y: 7 units

• x: 10 units, y: 0 units

• x: 5√3 units, y: 5 units

• x: 0 units, y: 10 units

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CCSS.HSN.VM.A.2

How do you add two vectors graphically?

• Add the two vectors by placing them end to end without any direction consideration.

• The resultant vector is obtained by drawing the first vector and then the second vector from the tip of the first.

• Multiply the magnitudes of the two vectors to find the resultant.

• Draw both vectors from the same starting point and connect their tails.

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CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

What is the significance of the direction in vector addition?

• The direction of vectors has no impact on the resultant vector.

• Only the magnitude of vectors matters in vector addition.

• The direction of vectors affects the resultant vector's magnitude and direction in vector addition.

• Vectors can be added without considering their direction.

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CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

If vector A = 5i + 3j and vector B = 2i - 4j, what is the resultant vector?

• 5i - 1j

• 3i + 7j

• 7i - 1j

• 4i + 3j

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CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

Describe the graphical method of vector resolution.

• Vector resolution is done by adding all vectors together without breaking them down.

• The graphical method involves only algebraic calculations without diagrams.

• The method requires the use of complex numbers instead of geometric representation.

• The graphical method of vector resolution involves drawing the vector, creating a right triangle with its components, and measuring the lengths of the components.

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CCSS.HSN.VM.A.2