Vectors and Scalars Quiz

<p>The magnitude (A)</p> Signup and view all the answers

<p>When they have the same magnitude and the same direction. (C)</p> Signup and view all the answers

<p>Displacement (D)</p> Signup and view all the answers

<p>Addition (D)</p> Signup and view all the answers

<p>East (D)</p> Signup and view all the answers

<p>Describing the diameter of a human hair in micrometers (µm). (A)</p> Signup and view all the answers

<p>To ensure that the equation is dimensionally consistent, reflecting a physically meaningful relationship. (D)</p> Signup and view all the answers

<p>To create a conversion factor that allows for changing from one unit to another without altering the quantity's inherent value. (C)</p> Signup and view all the answers

<p>The answer should have as many significant figures as the factor with the <em>least</em> significant figures. (C)</p> Signup and view all the answers

<p>The term with the fewest digits to the right of the decimal point. (A)</p> Signup and view all the answers

<p>A vector quantity has both magnitude and direction, while a scalar quantity only has magnitude. (C)</p> Signup and view all the answers

<p>$1 \times 10^{-3}$ kg (A)</p> Signup and view all the answers

<p>Both B and C (A)</p> Signup and view all the answers

<p>Magnitude-Direction and Components (B)</p> Signup and view all the answers

<p>Quadrant II (C)</p> Signup and view all the answers

<p>A vector with a length of 5 cm pointing along the positive x-axis. (B)</p> Signup and view all the answers

<p>Trigonometry (C)</p> Signup and view all the answers

<p>The x and y components of vector A, respectively. (D)</p> Signup and view all the answers

<p>$&lt;0, -10&gt;$ (C)</p> Signup and view all the answers

<p>Magnitude (A)</p> Signup and view all the answers

<p>It offers limited accuracy, especially for complex arrangements. (B)</p> Signup and view all the answers

<p>The vector's length and the angle it makes with a reference axis. (C)</p> Signup and view all the answers

<p>It changes both the magnitude and direction of the vector. (C)</p> Signup and view all the answers

<p>The vector from the tail of the first vector to the head of the last vector. (A)</p> Signup and view all the answers

<p>It's the same as adding $\vec{A}$ and $-\vec{B}$. (B)</p> Signup and view all the answers

<p>The resultant vector's magnitude and direction. (C)</p> Signup and view all the answers

<p>The order does not affect the resultant vector. (C)</p> Signup and view all the answers

<p>It involves finding the diagonal of a parallelogram formed by the two vectors. (B)</p> Signup and view all the answers

<p>The direction is undefined, since the resultant vector has zero magnitude. (C)</p> Signup and view all the answers

<p>One (A)</p> Signup and view all the answers

<p>The scalar product is negative. (C)</p> Signup and view all the answers

<p>−13 (B)</p> Signup and view all the answers

<p>A × B = −(B × A) indicates the vector product is anticommutative. (A)</p> Signup and view all the answers

<p>$θ = cos^{-1}((AxBx + AyBy) / |A||B|)$ (A)</p> Signup and view all the answers

<p>Work done by the force (A)</p> Signup and view all the answers

<p>1 (C)</p> Signup and view all the answers

<p>It can be used to find the angle between the two vectors. (A)</p> Signup and view all the answers

The International System of Units measuring length, time, and mass.

Prefixes help to create larger or smaller units for fundamental quantities.

1 kilometer is equal to 1,000 meters.

Digits that carry meaning contributing to measurement precision.

An equation must maintain consistent units throughout its terms.

Converting units via ratios to maintain accuracy in calculations.

Scalars are described by a number; vectors have magnitude and direction.

To convert minutes to seconds, use a ratio of 60 s per minute.

A quantity in physics that has magnitude only.

The size or length of a vector or scalar quantity.

A quantity that has both magnitude and direction.

The path along which something moves or indicates; important for vectors.

Vectors that have the same magnitude and direction.

A scalar quantity indicating how fast something is moving, measured in distance per time.

A scalar quantity that denotes how much space is between two points.

Vectors have two main characteristics: magnitude and direction.

A quantity in physics with both magnitude and direction.

A vector quantity indicating speed in a specific direction, e.g., 35 m/s, North.

A vector that indicates the rate of change of velocity, e.g., 10 m/s², South.

A graphical method for adding multiple vectors by placing the tail of one to the head of another.

A graphical method for subtracting vectors using the tip of one vector aligned with the tail of another.

Changing the magnitude of a vector without altering its direction by a scalar value.

The magnitude of a vector is calculated as A = √(Ax² + Ay²).

The direction of a vector can be found using tan(θ) = Ay/Ax.

The components of a vector's sum are Rx = Ax + Bx and Ry = Ay + By.

Unit vectors have a magnitude of 1 and indicate direction: î for x, ĵ for y, k̂ for z.

The scalar product of two vectors is the sum of the products of their corresponding components.

The angle between two vectors can be found using the scalar product formula: A·B = |A||B|cos(θ).

The vector product (cross product) produces a vector perpendicular to the plane formed by the original vectors.

The vector product is anticommutative: A × B = -B × A.

A method to describe a vector using its length and angle from the x-axis.

The x-component and y-component that represent a vector.

When the x or y values of a vector are above zero.

When the x or y values of a vector are below zero.

Calculating components from a vector's magnitude and direction.

A vector can be represented as A <3, 4> for components Ax and Ay.

Combining vectors visually may lead to inaccuracies.

The direction of the vector measured in degrees from the positive x-axis.