All you should know about vectors:
Try these 8 multiple-choice questions ...
Q1.
What is the standard trick to add two vectors graphically?
(a)
Translate vector nr. 2 such that its tail coincides with the tail of nr. 1
(b)
Take the length of the first one, find the square root, multiply with your age, do the same with the second one, then add these two numbers and divide by PI
(c)
Translate vector nr. 2 such that its tail coincides with the tip of nr. 1
(d)
You cannot add vectors, only subtract
Check one of
(a)
to
(d)
.
Q2.
Another way to add two vectors involves the vector components. What do you do?
(a)
Forget the components, they are totally useless
(b)
You add the x-component of nr. 1 to the x-component of nr. 2. This is the x-component of the result. The same goes for the y-components. Example: [2,3]+[3,4] = [5,7]
(c)
You add all coordinates [the length of the components] of nr. 1 and all coordinates of nr. 2 and make a big mess
(d)
You cannot add vectors, only subtract -- I said that already!
Check one of
(a)
to
(d)
.
Q3.
You have two vectors and you want to subtract one of them from the other. What do you do?
(a)
I take the opposite of one of them (which is always easy) and add this to the other one. It's really simple
(b)
Translate vector nr. 2 such that its tail coincides with the tip of nr. 1 (but wait a second, isn't this what I should do when I ADD?)
(c)
Translate vector nr. 2 such that its tail coincides with the tail of nr. 1 -- and then what?
(d)
You cannot subtract vectors, only add
Check one of
(a)
to
(d)
.
Q4.
Does this work also with components? For instance, what is [3,5]-[2.6]?
(a)
No, components are dangerous
(b)
0
(c)
100'000'000
(d)
Sure, take the opposite of the second one and add instead: [3,5]+[-2,-6] = [3-2,5-6] = [1,-1]
Check one of
(a)
to
(d)
.
Q5.
How is the scalar product of two vectors defined?
(a)
It is the product of the length of nr. 1 and the length of nr.2, and the cos of the angle formed by the two. Example: if nr. 1 has length 3 and nr. 2 has length 5 and the angle is 70 deg, the result is 5.13
(b)
It is the sum of the two vectors, and the sum vector you must multiply with the average length of the two vectors
(c)
It is the difference of the two vectors, and the difference vector you must multiply with the tan of the angle formed by the two vectors
(d)
It has something to do with the my bio rhythm
Check one of
(a)
to
(d)
.
Q6.
Consider two vectors, one with length a and the other with length b. And let us assume that the angle formed by the two vectors can be varied. What can you say about the scalar product when the angle varies from 0 deg to 180 deg?
(a)
For 0 deg angle, the scalar product is ab, and for 180 deg angle, the scalar product is 2ab
(b)
For 0 deg angle, the scalar product is 0, and for 180 deg angle the scalar product is 180ab
(c)
For 0 deg angle, the scalar product is ab. For 90 deg angle, the scalar product is 0. For 180 deg angle, the scalar product is -ab. If I plot the value of the scalar product as a function of the angle, the plot looks like the cos curve, with amplitude ab instead of 1
(d)
The scalar product does not depend on the angle
Check one of
(a)
to
(d)
.
Q7.
What can you do with components, when it comes to the scalar product of two vectors?
(a)
A lot! It turns out: You can multiply the components separately and add the results, and there you are! Such as: [a_x,a_y]*[b_x,b_y] = a_x b_x + a_y b_y. Example: [2,3]*[6,4] = 2*6+3*4 = 12+12 =24. Test: the lengths of the vectors are 3.61 and 7.21, angle is 22.62... it works!
(b)
Nothing. Components are useless anyway
(c)
What is components?
(d)
Components are good for adding and subtracting, ok, but for the scalar product?
Check one of
(a)
to
(d)
.
Q8.
What do you get if you have a vector and take the scalar product of that vector with the zero vector?
(a)
Always the original vector
(b)
Always the length of the original vector
(c)
0
(d)
Always the square of the length of the original vector
Check one of
(a)
to
(d)
.
Quiz devised by Gisle Kleppe, e-mail
gisle.kleppe@hsh.no
.
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on 30 August 2001 at 16:04