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Lab 1-Lines, Planes, and Distances: Objective: To Become Accustomed To MATLAB and To Use It To Study Some Basic

This document provides instructions and problems for a MATLAB lab on basic linear algebra concepts including lines, planes, and distances. Students are asked to use MATLAB to perform arithmetic operations, manipulate vectors, calculate lengths and angles between vectors, determine which vectors are parallel to a given plane, and find the intersection points (if any) between pairs of lines.

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84 views2 pages

Lab 1-Lines, Planes, and Distances: Objective: To Become Accustomed To MATLAB and To Use It To Study Some Basic

This document provides instructions and problems for a MATLAB lab on basic linear algebra concepts including lines, planes, and distances. Students are asked to use MATLAB to perform arithmetic operations, manipulate vectors, calculate lengths and angles between vectors, determine which vectors are parallel to a given plane, and find the intersection points (if any) between pairs of lines.

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Anonymous PDGLsjN1Q5
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© © All Rights Reserved
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Lab 1Lines, Planes, and Distances

Objective: To become accustomed to MATLAB and to use it to study some basic


properties of lines, planes, and distances.

MATLAB Commands:

Some Arithmetic and Trig:


x=7 Assign to x the value 7.
3*14/(4+2) Always use asterix (*) for multiplication, slash (/) for
division.
3^2 Use hat (^) for exponents.
sqrt(25) Square root function.
cos(pi) Use pi for . The other trig functions are similarly defined.
acos(1) Inverse cosine (arccos). Make inverse trig functions by
placing an a in front of the command for the trig function.
Some vector commands:
a=[12 5 -3] This creates the vector (12,5,-3) and gives it the name a.
b=(1/3)*[0 10 3] Creates vector (0,10/3,1). Notice how arithmetic is done
in MATLAB: Slash (/) for division and asterix (*) for
multiplication.
c=a/3+(2^3)*b More arithmetic. The hat (^) denotes exponentiation (so
2^3=8).
dot(a,b) Takes the dot product of two vectors a and b.

Submit your answers on paper to your TA for marking. For those questions that
involve the use of MATLAB, write down any relevant work involved in setting up
the problem and copy the solution from the screen to your answer sheet.

1. Practise basic MATLAB commands by using MATLAB to compute the


following quantities:
a) 35 / 6 2 (2.05)(1.96)
1
b)
2.54
c) 4(2, 3, 4) (2 5 / 9)(3.2,1.4, 1.5)
d) (3, 2, 4 / 3) ( 2.5, 7 / 4, 5)

1
e) sin(/6) (Note that by default MATLAB assumes angles are expressed i n
radians.)
f) arctan(0.8)
g) 3.4u 1.8v where u = (3.1, 4.2, 2.6) and v = (3.3, 4.1, 2.7) .

2. Find the length of each vector and the angle between each pair:
a) u = (2, 3) , v = (2,1)
b) u = ( 4, 2, 1) , v = (3 / 2, 0, 2)
c) u = (1.27, 2.33, 0.73) , v = (1.78, 0.66,1.22)

3. Which of the following vectors lies parallel to the plane 2 x1 4 x2 + 3 x3 = 0 ?


a) (4, 2, 7)
b) ( 3, 3 / 2, 4)
c) (2, 0, 3)

4. Find the points of intersection, if any, of the following lines:


a) x(t ) = (2, 3) + t (2, 4) and x( s) = (1,1) + s( 1, 2) in R 2.
b) x(t ) = (3, 4, 2) + t ( 2,1, 2) and x(u) = (1, 2, 4) + u(1, 4, 1) in R 3.
c) x( s) = (1, 3, 2) + s( 2,1,1) and x(u) = (3, 4, 2) + u(3, 0, 3) in R 3.
Which of the above pairs of lines are parallel?

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