vectr

Faz · #1 $Old$ November 21st, 2008, 08:10 AM

1)Find the distance between (1,-2,4) and (-2,3,0)
2)Find the magnitude of the vector
-> -> -> ->
W = 2i + j - 5k
3)Find the direction cosines of the vector
-> -> -> ->
W = 2i + j - 5k

Plse help step by step thks.

Chris L T521 · #2 $Old$ November 21st, 2008, 08:20 AM

Quote:

Originally Posted by Faz $View Post$

1)Find the distance between (1,-2,4) and (-2,3,0)

The distance between two points is defined as : $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Can you try to take it from here?

Quote:

2)Find the magnitude of the vector
-> -> -> ->
W = 2i + j - 5k

To find magnitude, we see that $||\mathbf{w}||=\sqrt{w_x^2+w_y^2+w_z^2}=\dots$

Can you continue?

Quote:

3)Find the direction cosines of the vector
-> -> -> ->
W = 2i + j - 5k

Plse help step by step thks.

Since you already have the magnitude of this vector, things will work out nicely.

Direction cosines are defined as follows:

If you want the angle between the vector and the x axis, use $\cos\alpha=\frac{w_x}{||\mathbf{w}||}$

If you want the angle between the vector and the y axis, use $\cos\beta=\frac{w_y}{||\mathbf{w}||}$

If you want the angle between the vector and the z axis, use $\cos\gamma=\frac{w_z}{||\mathbf{w}||}$

Then you can easily find $\alpha,~\beta$ , and $\gamma$

Can you try to take it from here?

--Chris