# Don't know how to do the vector sign

I have been having a really rough time on my 3 homework problems tonight...I don't really understand vectors, so any help would be appreciated!

Sorry about the no LaTeX, I don't know how to do the vector sign

Anyway...

1.Given the Vectors U=2i(hat)-3j(hat)= <2,-3> and
V=-i(hat)+4j(hat)= <-1,4>, find:
a. U+V
b. 2U-3V
c. $$|V-U|$$

2.Draw a sketch to find each of the following graphically. (P and Q are in the attachment)
a. P+Q
b. P-3Q
c. -4P+4Q

On this one, my friend told me just to basically draw a triangle for each one of the problems, and the added third line to complete the triangle would equal the resultant vector. Is this right?

3.An airplane pilor needs to fly to a point 1800 km due east in a time of 6.0 hours. If a steady wind is blowing at 60 km/h from due south towards due north, calculate the velocity of the plane relative to the air (specifying both magnitude and direction) needed to achieve the pilot's objective.

I don't really know how side-winds affect flying objects being propelled at those speeds, some explanation on that would be appreciated to help solve the problem.

Thanks for your time taken for the help!

#### Attachments

• Vectors for Question 2.JPG
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For the first one, change it matrices form which makes it easier to calculate and you simply and them or subtract them like you would with normal matrices.

Second, yes that would work. Make sure you've got the direction arrows right though.

Third, try resolving it in terms of vertical and horizontal. Basicaly, draw a diagram, that always work.

andrevdh
Homework Helper
$$U = 2 \hat{i} - 3\hat{j}$$

$$V = -1\hat{i} + 4\hat{j}$$

a) $$U + V = 1\hat{i} + 1\hat{j}$$

see attachment for b)

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'I don't really know how side-winds affect flying objects being propelled at those speeds, some explanation on that would be appreciated to help solve the problem. '

If your objective is due East, in what direction do you travel to get to that destination if a sidewind is trying to push you Northwards? If you just travel due East you will end up North of your destination...

andrevdh
Homework Helper
Lets say that the airplane is flying along vector $$\vec{v_a}$$ and the wind is blowing along the vector $$\vec{v_w}$$ and his objective is to fly along $$\vec{v_o}$$. Then

$$\vec{V_o} = \vec{V_a} + \vec{V_w}$$

and since we know the magnitude and direction of the objective and wind vectors we require

$$\vec{V_a} = \vec{V_o} - \vec{V_w}$$

HallsofIvy