1. [SOLVED] help

hi i would like to ask a few vector questions but i dont know where
to ask so is it ok if i open a new thread?
can someone explain to me how to do this questions?

1.find the distance from (3,7,-5) to the xy-plane, xz-plane, and yz-plane.

2.a rope is tied 8m apart,and when a wet shirt with mass of 0.8kg is hung at the middle of the line,the midpoint is pulled down 8cm.find the tension is each half of the rope.

3.a woman walks due west on a ship at 3mi/h. the ship is moving north at a speed of 22mi/h.find the speed and direction of woman relative to the surface of the water.

4.if r= (x,y,z), a= (a1,a2,a3) and b= (b1,b2,b3) show the vector equation (r-a).(r-b) = 0 represents a sphere,find its center n radius.

2. Originally Posted by garlikk
hi i would like to ask a few vector questions but i dont know where
to ask so is it ok if i open a new thread?
can someone explain to me how to do this questions?

1.find the distance from (3,7,-5) to the xy-plane, xz-plane, and yz-plane.
in the xy-plane, the z-component is 0. so use the distance formula to find the distance between (3,7,-5) and (3,7,0)

similarly, for the xz-plane, find the distance between (3,7,-5) and (3,0,-5)

and for the yz-plane, find the distance between (3,7,-5) and (0,7,-5)

2.a rope is tied 8m apart,and when a wet shirt with mass of 0.8kg is hung at the middle of the line,the midpoint is pulled down 8cm.find the tension is each half of the rope.
this site looks neat. draw your diagram, fill in the required measurements, enter then in the required fields and follow the solution given.
4.if r= (x,y,z), a= (a1,a2,a3) and b= (b1,b2,b3) show the vector equation (r-a).(r-b) = 0 represents a sphere,find its center n radius.

plug in the points, you will get:

$\left< x - a_1, y - a_2, z - a_3 \right> \cdot \left = 0$

take the dot product and simplify to get the form: $(x - h)^2 + (y - k)^2 + (z - m)^2 = R^2$

the center is (h,k,m) and the radius is R

3. Originally Posted by garlikk
3.a woman walks due west on a ship at 3mi/h. the ship is moving north at a speed of 22mi/h.find the speed and direction of woman relative to the surface of the water.
your diagram is a right-triangle with base 3 and height 22. do you see how i got that? can you continue the problem? the magnitude of the hypotenuse will give the speed, while traveling along the hypotenuse from the end of the 22-length side to the end of the 3-length side will give you the direction. to have the precise direction, you may want to give it in terms of bearings, which means you need to find the required angles in the triangle

4. Originally Posted by Jhevon
in the xy-plane, the z-component is 0. so use the distance formula to find the distance between (3,7,-5) and (3,7,0)

similarly, for the xz-plane, find the distance between (3,7,-5) and (3,0,-5)

and for the yz-plane, find the distance between (3,7,-5) and (0,7,-5)

this site looks neat. draw your diagram, fill in the required measurements, enter then in the required fields and follow the solution given.
plug in the points, you will get:

$\left< x - a_1, y - a_2, z - a_3 \right> \cdot \left = 0$

take the dot product and simplify to get the form: $(x - h)^2 + (y - k)^2 + (z - m)^2 = R^2$

the center is (h,k,m) and the radius is R
hi thnx for these solutions,
but for the site that you give,it cant help me solve the problem.
you see,my question has no angle given.
i tried using tan theta,but the answer comes out weird. ;(

and for the last question,i expand the dot product but then i dont know how to simplify it!
help!

5. and these are few more questions if someone can help~

1. what's the meaning of N50 degree W?

2.a wrench 30cm lies along positive y-axis and grips at origin.a force is applied in direction (0,3,-4) at the end of wrench.find the magnitude of force to produce torque of 100Nm. i tried doing this but how to find the angle of the force?

3. let P be a point not on line L which passes thru points Q and R.Show the distance from point P to line L is :

distance = I axb I where a = QR and b = QP
I a I

*the symbol 'I' is modulus.

4.find lengths of medians of triangles with vertices A(1,2,3), B(-2,0.5)
and C(4,1,5)

5.find equation of largest sphere with center (5,4,9) in first octant.
is the answer (x-5)^2 + (y-4)^3 + (z-9)^2 = 0?

thnx!!!

6. Originally Posted by garlikk
hi thnx for these solutions,
but for the site that you give,it cant help me solve the problem.
you see,my question has no angle given.
i tried using tan theta,but the answer comes out weird. ;(
if you drew a diagram, you can find the angles. you would have two right-triangles where you know the opposite and adjacent sides to the angles shown

and for the last question,i expand the dot product but then i dont know how to simplify it!
help!
you expanded everything fully and don't see where to go? do you remember how to complete the square?

$\left< x - a_1, y - a_2, z - a_3 \right> \cdot \left< x - b_1, y - b_2 , z - b_3 \right> = 0$

$\Rightarrow (x - a_1)(x - b_1) + (y - a_2)(y - b_2) + (z - a_3)(z - b_3) = 0$

$\Rightarrow x^2 - (a_1 + b_1)x + a_1b_1 + y^2 - (a_2 + b_2)y + a_2b_2 + z^2 - (a_3 + b_3)z + a_3b_3 = 0$

$\Rightarrow [x^2 - (a_1 + b_1)x] + [y^2 - (a_2 + b_2)y] + [z^2 - (a_3 + b_3)z] = -(a_1b_1 + a_2b_2 + a_3b_3)$

Now complete the square of all the terms in the square brackets, you will get something in the required form after you simplify nicely

7. Originally Posted by garlikk
and these are few more questions if someone can help~

1. what's the meaning of N50 degree W?

2.a wrench 30cm lies along positive y-axis and grips at origin.a force is applied in direction (0,3,-4) at the end of wrench.find the magnitude of force to produce torque of 100Nm. i tried doing this but how to find the angle of the force?

3. let P be a point not on line L which passes thru points Q and R.Show the distance from point P to line L is :

distance = I axb I where a = QR and b = QP
I a I

*the symbol 'I' is modulus.

4.find lengths of medians of triangles with vertices A(1,2,3), B(-2,0.5)
and C(4,1,5)

5.find equation of largest sphere with center (5,4,9) in first octant.
is the answer (x-5)^2 + (y-4)^3 + (z-9)^2 = 0?

thnx!!!
to have a better chance of being seen. you should post new questions in a new thread.

delete this post and copy the questions (except the two i answered) to a new thread.

just a quick answer for number 1

N $50^o$ W is a way to measure direction. it means we start looking north, turn $50^o$ to the westerly direction. the direction in which we face is the direction we want

for 5, it helps to draw sketches for problems like these. you know where the first octant is, right? you want to make sure the radius is the smallest distance from the center to any of the axis

,

,

(r-a) dot (r-b)

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