<p>Okay I am having trouble with these problems..
1. Given u= <3,2,1> & v= <3,-1,2> & w= <7,-1,2> find vector z where z= 3u-v+3w
A) what is the z component:________
And linear form of the standard unit of z:______</p>
<ol>
<li><p>Calculate the angle between u=2i-j+k and v=-3i+2j+2k
Angle between u and v is _____ degrees</p></li>
<li><p>Identify if the pair if vectors is orthogonal, parallel or neither
A) u=i+2j+3k V=-i+2j-k
B) u=4i-2j+12k v=6i-3j+18k</p></li>
<li><p>Find the area of a parallelogram that has the vectors as adjacent sides u=2i-4j-3k and v=-i+2j+2k</p></li>
<li><p>Find the volume of the prism formed by three vectors: u=3i-j+2k v=2i+j+5k and w=i-2j-2k</p></li>
<li><p>Find the equation of the plane that passes through the points (2,1,-4) (-3,1,3) and (-2,-1,0) and how would you test the point?</p></li>
<li><p>Calculate the distance between the points (2,-1,-2) and plane 2x-3y+z=2</p></li>
<li><p>Find The angle between the two planes 4x-y+z=0 and 2x+y+3z=0</p></li>
</ol>
<p>Thanks in advance!!</p>
<p>I highly doubt those are ACT Math questions.</p>
<p>Maybe not specifically but this is what my current act/sat prep class is going over. Can anyone help?</p>
<p>Don’t bother doing these problems, and ask your act prep teacher why he/she is covering material that WILL NOT be found on the test. This is college-level linear algebra.</p>
<p>Not sure if the SAT covers this or not. Probably NOT.</p>
<p>1.) <27,4,7>
{<27,4,7>} / sqrt(794)</p>
<p>2.) @= arccos[ (uv) / |u||v| ]
@=arccos[-6 / sqrt(102)]
@=126.45 degrees</p>
<p>3.) a) neither
b) parallel</p>
<p>4.)jesus…ur makin me work…
the marea is the magnitude of their cross product vector:
sqrt(117) units squared</p>
<p>5.)I’m assuming this one is defining a parallelepiped.
the volume is U(VxW)
basically you can just set up a matrix with each row consisting of the coordinates of one of the vectors. then you find the determinant of
said matrix
I got 5 units cubed</p>
<p>6.) Basically you just make two vectors from the points. However, they both have to share their inital or terminal point (not both, then theyd be the same vector)
Then you find the cross product, but instead of being in terms of i, j, and k; it will be x, y, and z instead, respectively
Then set it equal to zero, but first add an external variable (D is what my precalc teacher used) and plug in one of the inital 3 points’ coordinates then solve for D. Ill show you what I mean with the real numbers:
14x-8y+10z+D=0
use any of the 3 points in the equation
You will get D=20
Thus the answer is:
14x-8y+10z+20=0</p>
<p>7.) I want to explain this to you, but it’s really a pain in the ass. Look up the equation, ill just tell you the answer:
3 / sqrt(14)</p>
<p>8.)Once again, look up the formula, ill tell you the answer:
arccos[10 / 3sqrt(28)]
which is 50.95 degrees</p>
<p>Just want to say…ive taken the ACT and there was nothing about vectors in the math section. Certainly the SATdoes not either, which barely even incorporates algebra 2. If you are preparing for the ACT, id suggest you go over algebra 1/2, geometry, and precalc. The ACT math is something you CAN study for, but shouldnt have to.</p>
<p>How to get people to do your math homework: tell people it’s a question from the ACT.</p>
<p>LOL.</p>
<p>How to mess with people’s minds when they take advantage of you to try and get answers for their homework: Make up a solution/answer and make them realize that they need to figure out how to do their own homework after they get a zero on that assignment.</p>
<p>LOL.</p>
<ol>
<li><p>is really easy, just do it component by component. e.g. 3<3,2,1> - <3,-1,2> + 3<7,-1,2> = <27,4,7></p></li>
<li><p>You need the dot product, u * v = |u||v|cos(x) where x is the angle between u and v</p></li>
<li><p>A, neither. B, one’s just a scalar multiple of the other. parallel.</p></li>
<li><p>Area of the parallelogram is just the magnitude of the cross product of the vectors.</p></li>
</ol>
<p>5 - 8 my linear algebra sucks (that’s why I’ll be taking it next year). I know there are simple formulas for finding the volume of the prism (I believe it’s the determinant of the 3x3 matrix formed by the vectors) but you can refer to ratmkino’s solutions or look online/in your textbook.</p>