Exam 1: Introduction and Vectors

What two vectors are each the same magnitude as and perpendicular to $7 \tilde { \mathbf { i } } + 24 \hat { \mathbf { j } }$ ?

A rectangle has a length of 1.323 m and a width of 4.16 m.Using significant figure rules,what is the area of this rectangle?

If two collinear vectors $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ are added,the resultant has a magnitude equal to 4.0.If $\overrightarrow { \mathbf { B } }$ is subtracted from $\overrightarrow { \mathrm { A } }$ ,the resultant has a magnitude equal to 8.0.What is the magnitude of $\overrightarrow { \mathrm { A } }$ ?

Find the average density of a red giant star with a mass of 20 * 10³⁰ kg (approximately 10 solar masses)and a radius of 150 *10⁹ m (equal to the Earth's distance from the sun).

The quantity with the same units as force times time,Ft,with dimensions MLT ^{- 1} is

Vectors $\overrightarrow { \mathbf { A } }$ and $\vec { B }$ are shown.What is the magnitude of a vector $\overrightarrow { \mathrm { C } }$ if $\overrightarrow { \mathrm { C } } = \overrightarrow { \mathrm { A } } - \overrightarrow { \mathrm { B } }$ ?

Which quantity can be converted from the English system to the metric system by the conversion factor $\frac { 5280 \mathrm { f } } { \mathrm { mi } } \cdot \frac { 12 \mathrm { in } } { \mathrm { f } } \cdot \frac { 2.54 \mathrm {~cm} } { 1 \mathrm { in } } \cdot \frac { 1 \mathrm {~m} } { 100 \mathrm {~cm} } \cdot \frac { 1 \mathrm {~h} } { 3600 \mathrm {~s} }$ ?

Dana says any vector $\overrightarrow { \mathrm { R } }$ can be represented as the sum of two vectors: $\overrightarrow { \mathbf { R } } = \overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { B } }$ .Ardis says any vector $\overrightarrow { \mathrm { R } }$ can be represented as the difference of two vectors: $\overrightarrow { \mathbf { R } } = \overrightarrow { \mathrm { A } } - \overrightarrow { \mathbf { B } }$ .Which one,if either,is correct?

Which of the following quantities has the same dimensions as kinetic energy, $\frac { 1 } { 2 } m v ^ { 2 }$ ? Note: [a] = [g] = LT ^{- 2};[h] = L and [v] = LT ^{- 1}.

Two vectors starting at the same origin have equal and opposite x components.Is it possible for the two vectors to be perpendicular to each other? Justify your answer.

John and Linda are arguing about the definition of density.John says the density of an object is proportional to its mass.Linda says the object's mass is proportional to its density and to its volume.Which one,if either,is correct?

Exhibit 3-3 The vectors $\overrightarrow { \mathrm { A } }$ , $\vec { B }$ ,and $\overrightarrow { \mathrm { C } }$ are shown below. Use this exhibit to answer the following question(s). -Refer to Exhibit 3-3.Which diagram below correctly represents $\overrightarrow { \mathbf { A } } + \overrightarrow { \mathbf { B } } + \overrightarrow { \mathbf { C } }$ ?

The displacement of the tip of the 10 cm long minute hand of a clock between 12:15 A.M.and 12:45 P.M.is:

The term $\frac { 1 } { 2 } \rho v ^ { 2 }$ occurs in Bernoulli's equation in Chapter 15,with $\rho$ being the density of a fluid and v its speed.The dimensions of this term are

Adding vectors $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ by the graphical method gives the same result for $\overrightarrow { \mathrm { A } }$ + $\vec { B }$ and $\vec { B }$ + $\overrightarrow { \mathrm { A } }$ If both additions are done graphically from the same origin,the resultant is the vector that goes from the tail of the first vector to the tip of the second vector,i.e,it is represented by a diagonal of the parallelogram formed by showing both additions in the same figure.Note that a parallelogram has 2 diagonals.Keara says that the sum of two vectors by the parallelogram method is $\overrightarrow { \mathbf { R } } = 5 \hat { \mathbf { i } }$ Shamu says it is $\overrightarrow { \mathbf { R } } = \hat { \mathbf { i } } + 4 \hat { \mathbf { j } }$ Both used the parallelogram method,but one used the wrong diagonal.Which one of the vector pairs below contains the original two vectors?

Which one of the quantities below has dimensions equal to $\left[ \frac { \mathrm { ML } } { \mathrm { T } ^ { 2 } } \right]$ ?

When vector $\overrightarrow { \mathrm { A } }$ is added to vector $\vec { B }$ ,which has a magnitude of 5.0,the vector representing their sum is perpendicular to $\overrightarrow { \mathrm { A } }$ and has a magnitude that is twice that of $\overrightarrow { \mathrm { A } }$ .What is the magnitude of $\overrightarrow { \mathrm { A } }$ ?

A vector $\overrightarrow { \mathrm { A } }$ is added to $\overrightarrow { \mathbf { B } } = 6 \hat { \mathbf { i } } - 8 \hat { \mathbf { j } }$ .The resultant vector is in the positive x direction and has a magnitude equal to that of $\overrightarrow { \mathrm { A } }$ .What is the direction of $\overrightarrow { \mathrm { A } }$ ?

Anthony has added the vectors listed below and gotten the result $\overrightarrow { \mathbf { R } } = 9 \hat { \mathbf { i } } + 4 \hat { \mathbf { j } } + 6 \hat { \mathbf { k } }$ .What errors has he made? $\overrightarrow { \mathbf { A } } = 3 \tilde { \mathbf { i } } + 4 \tilde{ \mathbf { j } } - 5 \tilde { \mathbf { k } }$ $\overrightarrow { \mathbf { B } } = - 3 \hat { \mathbf { i } } + 2 \hat { \mathbf { j } } + 8 \hat { \mathbf { k } }$ $\overrightarrow { \mathbf { C } } = 3 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } } + 2 \hat { \mathbf { k } }$

If two collinear vectors $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ are added,the resultant has a magnitude equal to 4.0.If $\vec { B }$ is subtracted from $\overrightarrow { \mathrm { A } }$ ,the resultant has a magnitude equal to 8.0.What is the magnitude of $\overrightarrow { \mathrm { A } }$ ?