Any vectors expert??? answer this with explaination?

Question

1) Force = 6i - 3j + 10k Newton producing an acceleration of 1m/s2
then the mass of the body would be????

2) What angle will vector A =2i + 3j make with the Y-axis

i, j and k are unit vectors along the X,Y and Z axis.

Answer 1

Yes, the force is represented by unit vectors (sorry, im not familiar with terms in english sometimes :p)

a)Square [6² + (-3)² + 10²] = 12.04N. That means the total magnitud of the force.

Now, you say: F = ma; so
12.04N = 12.04kg*m/s² = mass(1m/s²) and you'll end up with:

mass = (12.04kg*m*s²)/(1m*s²) = 12.04kg


b)the vector A is on the x-y dimentions only. If you plot it, you'll see it like this:
http://img446.imageshack.us/img446/2359/vectorajg9.jpg
Two units to along the x-axis, three units along the y-axis. There you go. Now the vector meets the intersection of them.

So, now you can use a trigonometric function, lets say tan(Θ) = y/x.

tan (Θ) = 3/2 = 1.5
Θ = tanֿ¹ (1.5) = 56.31º

Answer 2

1) First you have to figure out the total force. This equation describes in directionally. To find just the force:
square root (6^2 + 3^2 + 10^2) = squareroot 145 = 12.04 N

Then use the equation F=ma to find the mass.
12.04 N = m (1 m/s^2)
m = 12.04 kg


2) This vector simply states that a lines starts from any point. It travels two units in the x direction and 3 units in the y direction. The length of the vector is the squareroot of (2^2 + 3^2) or 3.61. For simplicity, make the vector's starting point be the origin (0,0). If you plot it, you will have a right triangle with base 2 and height 3. Use the law of sines to find the angle at the origin.
(sin a)/A = (sin b)/B
sin of 90 degrees is 1. The length of the hypotenuse is 3.61.
sin of the interior angle (b) is unknown. The length of the opposite side is 3.
Therefore, sin b = (sin a)B/A = 1 (3)/3.61 = 0.831.
b = 56.2 degrees

Answer 3

"wyo_me" does a good job explaining it.


The "i", "j", and "k" notation do not represent complex numbers in this case (although I can understand how you could make the mistake). The "i j k" notation is used to indicate unit vector notation.
The "i" unit vector has a magnitude of 1 unit in the x direction. The "j" unit vector has a magnitude of 1 in the y direction. The "k" unit vector, you guessed it, has a magnitude of 1 in the z direction.
When we write 6i - 3j + 10k is means a vector with an x component of magnitude 6 (in the + direction), a y component with magnitude 3 in the negative direction, and a z component with magnitude 10 (in the + direction).
To get the overall magnitude of the vector, just add the squares and take the square root (apply the Pythagorean Theorem).

Answer 4

1)the magnitude is given by [(6)^2+(-3)^2+(10)^2]^1/2=(145)^1/2
mass =F/a,substituting=(145)^1/2 kg

2) the unit vector in the direction of the given vector=2i+3j/(13)^1/2=2/(13)^1/2i+3/(13)^1/2j and so the direction cosines are(2/[(13)^1/2,3/(13)^1/2,0]

Answer 5

"6i" seems to be part of a complex number, as expressed by mathematicians.
"3j" would also be part of a complex number, but for electricians, whom use "j" instead of "i" (since i is symbol for current).
Your expression is unclear.
F = m * a.
If you know the force and the acceleration, then the mass is F/a.
A force is defined as a value (in Newtons) AND a vector (that may be expressed in a vectorial form or complex form), but not in the same formula!