Addition and Subtraction of Vectors

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What is a vector in mathematics?

A vector is a quantity with both magnitude and direction.

How do you add two vectors?

Place the tail of the second vector at the head of the first and draw the resultant from the tail of the first to the head of the second.

What is the resultant vector?

It's the vector that represents the sum of two or more vectors.

How do you subtract vectors?

Reverse the direction of the vector to be subtracted, then add it to the first vector.

Can vectors be added algebraically?

Yes, by adding corresponding components of the vectors.

What are unit vectors?

Vectors with a magnitude of 1, used to represent direction.

How do you find the magnitude of a vector?

Use the formula √(x² + y²) for a vector with components x and y.

What does the term 'vector component' mean?

It's the projection of a vector along the axes of a coordinate system.

How does the parallelogram method work for vector addition?

Place vectors with the same initial point, complete a parallelogram, diagonal is the sum.

What is the triangle method in vector addition?

Placing vectors head to tail to form a triangle, with the closing side as the resultant.

Why are vectors important in physics?

They describe physical quantities with direction and magnitude, like force and velocity.

What are orthogonal vectors?

Vectors that are at right angles to each other, having a dot product of zero.

Can vectors in different dimensions be added directly?

No, vectors must be within the same dimensional space to be added.

What role do coordinates play in vector operations?

They determine the position from which vector calculations start.

What does vector notation look like?

Vectors are often written in bold or with an arrow above, like \(\vec{a}\) or \(\mathbf{a}\).


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1. What is a vector in mathematics?

A scalar quantity with only magnitude.

A vector is a quantity with both magnitude and direction.

A type of animal with unique patterns.

An object with no measurable properties.

2. How do you add two vectors?

Draw a circle around them and measure the circumference.

Stack one on top of the other and calculate the density.

Use a graphing calculator to find the intersecting point.

Place the tail of the second vector at the head of the first and draw the resultant from the tail of the first to the head of the second.

3. What is the resultant vector?

It's the vector that represents the sum of two or more vectors.

The vector that represents the south direction only.

A vector that cancels out the original vector.

The second component of a vector pair.

4. How do you subtract vectors?

By removing them completely from the calculation.

Cross multiplication of components.

Adding their magnitudes directly.

Reverse the direction of the vector to be subtracted, then add it to the first vector.

5. Can vectors be added algebraically?

No, vectors can only be combined geometrically.

Only when they are in a different plane.

Yes, by adding corresponding components of the vectors.

Only by subtracting their scalars first.

6. What are unit vectors?

Vectors with a magnitude of 1, used to represent direction.

Vectors with a magnitude of infinity.

Vectors that represent zero direction.

Any vector that exceeds three dimensions.

7. How do you find the magnitude of a vector?

Use the formula √(x² + y²) for a vector with components x and y.

Multiply the vector by 10.

Subtract the y component from the x component.

Combine the vector components and take the square root of their sum.

8. What does the term 'vector component' mean?

It's the projection of a vector along the axes of a coordinate system.

A single line from vector zero to vector one.

The constant speed of a vector.

Any part of a vector situated outside its central axis.

9. How does the parallelogram method work for vector addition?

Place vectors with the same initial point, complete a parallelogram, diagonal is the sum.

Align vectors parallel to each other and double their length.

Reverse one vector and sum up their magnitudes.

Draw a hexagon around them to visualize direction.

10. What is the triangle method in vector addition?

Placing vectors head to tail to form a triangle, with the closing side as the resultant.

Hook vectors together at the midpoint for symmetry.

Use three vectors combined to find the middle angle.

Align vectors in a circular diagram.

11. Why are vectors important in physics?

They help visualize temperature changes.

They describe physical quantities with direction and magnitude, like force and velocity.

Vectors only matter in historical physics studies.

Vectors function as decoration in equations.

12. What are orthogonal vectors?

Vectors that are at right angles to each other, having a dot product of zero.

Vectors on a spiral path.

Vectors with only magnitude, no direction.

Any vectors that are parallel whenever possible.

13. Can vectors in different dimensions be added directly?

Yes, by ignoring extra dimensions.

No, vectors must be within the same dimensional space to be added.

Only if they sum to zero.

By adding dimensions with similar values.

14. What role do coordinates play in vector operations?

They provide colors for graphical representations.

They determine the position from which vector calculations start.

Coordinates add confusion rather than clarity.

Coordinates denote the end of the vector.

15. What does vector notation look like?

Vectors are noted as plain numbers without direction.

Vectors are often written in bold or with an arrow above, like \(\vec{a}\) or \(\mathbf{a}\).

Vectors are enclosed in square brackets.

Any alphabetical letter without enhancements.