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Practice: Magnitude of a Vector

Related Topics

Wize University Physics Textbook (Master) > Introduction to Vectors

Vectors and Their Components

6 Activities

Wize University Linear Algebra Textbook > Vectors

Vector Properties

4 Activities

Practice: Magnitude of a Vector

An aircraft's location is 200 miles from base, at a direction of 30° W of S, at an altitude of 35,000 ft. Find the distance between the aircraft and the base.

Note: 1 mile = 5280 feet
More Vectors and Their Components Questions:
I'm moving and packed all my books into a box that weighs 17kg. I pull the box on a weightless dolly with a force of 60N at an angle of 30° to the horizontal surface.
a) What is the acceleration of the box?
b) The box feels the normal force from the ground and the force of gravity. Are the normal force and gravity an action-reaction pair? Explain your answer!
Vector arithmetic practice
Consider the vectors a⃗=−2i^+3j^−k^;   b⃗=4i^+3k^;   c⃗=−i^+3j^−k^\vec a=-2\hat i+3\hat j-\hat k; ~~~\vec b= 4\hat i+3\hat k; ~~~ \vec c=-\hat i+3\hat j-\hat k.
a) For each of these three vectors, find the magnitude.
b) For each of these three vectors, find a unit vector pointing in the same direction.
Component vectors practice
You try to pull a heavy box by attaching a rope and pulling with a force of 20.0 N at an angle of 13.4 degrees above horizontal. What are the components of this force in the horizontal and vertical directions? Draw a diagram to support your answer.
A rabbit, escaping a fox, runs 40o north of west at 10.0m/s. A coordinate system is established with the positive x-axis to the east and the positive y-axis to the north. Write the rabbit’s velocity in terms of components and unit vectors.
Break into components
Given a velocity of 5.0m/s at 40.0o above the -x axis:
Which of the following is an example of a vector quantity?
Which of the following operations will not change a vector?
Practice Vector Components
Find horizontal and vertical components of a vector R shown in the Figure.
A bowling ball with mass of 1 kg travelling at 0.75 m/s hits a 0.5 kg bowling pin, initially at rest. The bowling pin moves off with a speed of 0.25 m/s at an angle of 35º relative to the initial direction of the bowling ball. What is the final velocity of the bowling ball? (note: you cannot assume kinetic energy is conserved).
Particle m1 with mass of 4×10−254 \times 10^{-25}kg is travelling with a velocity of 5msi^5\frac{m}s\hat i , and collides with particle m2 with mass 6×10−25 kg6\times 10^{-25}~\rm kg which is initially at rest. After the interaction, m1 travels with speed of 5 m/s at an angle of 45 degrees with vector.
What is the total momentum of the system?
What is the vector velocity of m2?
More Vector Properties Questions:
Practice: Vector Addition and Subtraction
The coordinates of four corners of a Parallelogram ABCDABCD in a Clock-Wise order are A=(1,3)A=(1,3), B=(−1,5)B=(-1,5), CC and D=(4,7)D=(4,7). Find missing coordinates of CC.
$\tkct{cut from 19.4F}$ Mid $\tkco{ S}$ | 133 - FML 3 - 18.1W e.g. 45
Given the points P=(3, 4, −1)\bcb{P = (3,\, 4,\, -1)} and Q=(−1, 2, 2)\bcb{Q = (-1,\, 2,\, 2)}, and the vector u⃗=PQ⃗\bcb{\ol{u} = \vec{PQ}}, find a vector parallel but in the opposite direction to u⃗\bcb{\vec{u}}.
Length / magnitude / norm. 19.1W
1. Find the vector d⃗\vd connecting the points P1(−2,−1)P_1(-2,-1) and P2(3,11)P_2(3,11).
2. Find the length of the vector d⃗\vd found, above. What does this length represent?
A parallelogram in R3R^3 has vertices A(−1,1,2)A\left(-1,1,2\right), B(1,−2,8)B\left(1,-2,8\right) and C=(3,−1,2)C=\left(3,-1,2\right).
Vector Arithmetic
Suppose X=(x1,x2,x3)X=(x_1, x_2, x_3) and Y=(y1,y2,y3)Y=(y_1, y_2, y_3) If −XY⃗=<43,−35,103>\vec{-XY}=\left<\frac{4}{3},\frac{-3}{5}, \frac{10}{3}\right>, what is YX⃗\vec{YX}?
Practice Question 9: Vector Operations
Practice Question: Vector Operations
Let u⃗=(−9, 6)\vec{u}=\left(-9,\ 6\right) and v⃗=(1,−1)\vec{v}=\left(1,-1\right). If we start at the origin and travel along a directed line segment that is opposite to u⃗\vec{u} but has 1/3 of its length, then we travel along the translation of v⃗\vec{v} to your current position. Finally, we travel along the translation of the unit vector that points in the same direction as v⃗\vec{v}.
a.) Where do we end up?
If α∈R\alpha \in \mathbb{R} and v∈Vv \in V , where VV is a real vector space and αv=0\alpha v = 0 , then prove that either α=0\alpha = 0 or v=0v = 0 .
Practice: Vector Addition and Subtraction
The coordinates of four corners of a Parallelogram ABCDABCD in a Clock-Wise order are A=(1,3)A=(1,3), B=(−1,5)B=(-1,5), CC and D=(4,7)D=(4,7). Find missing coordinates of CC.
Practice Question: Vector Properties
Practice Question: Vector Properties
Given that u⃗\vec{u} and v⃗\vec{v} are vectors in R3\mathbb{R}^3, which of the following statements is/are always true?
Practice: Vector Operations
A parallelogram has sides ABAB, BCBC, CDCD and DADA
The following coordinates are known: A(2,0,1)A(2,0,1), C(6,0,0)C(6,0,0), and M(3,1,0)M(3,1,0), where MM is the midpoint between AA and BB
Find the vector BD⃗\vec{BD}