# Thread: NEED HINTS ON THOSE PROBLEM--VECTOR

1. ## NEED HINTS ON THOSE PROBLEM--VECTOR

MIDTERM IS COMING..

NEED SOME GENERAL EXAMPLE OF SOME PROBLEM.

HELP APPRECIATED

2. Originally Posted by yzc717
MIDTERM IS COMING..

NEED SOME GENERAL EXAMPLE OF SOME PROBLEM.

HELP APPRECIATED

Hint for 1:

the vector parallel to the vector a is a constant times the vector a. a vector perpendicular to a is one for which its dot product with a is zero

you want these two vectors to add and give you b, you will have to solve for some unknowns

Hint for 2: if the plane is parallel, it has the same normal vector, namely <1,3,-5>.

a plane with normal vector $\displaystyle \vec n = <a,b,c>$ passing through a point $\displaystyle (x_0,y_0,z_0)$ is given by

$\displaystyle a(x - x_0) + b(y - y_0) + c(z - z_0) = 0$

the distance, $\displaystyle D$, from a point $\displaystyle (x_0,y_0,z_0)$ to a plane $\displaystyle ax + bx + cz + d = 0$ is given by:

$\displaystyle D = \frac {ax_0 + by_0 + cz_0 + d}{\sqrt{a^2 + b^2 + c^2}}$

Hint for 3: find c, let $\displaystyle c = <c_1,c_2,c_3>$ and take its dot product with b and find the vector when you subtract it from a, set the two vectors equal and solve for the components

Hint for 4: do the computation and set it equal zero. you should be able to see if this describes a line or not.

then set the same computation to a nonzero constant, show that you can't get a line

Hint for 5: come on, finding determinants is something you can look up, quite easily. google is your friend.

Hint for 6: again, something you can look up.

3. can anyone show me the solution for problem1 and 3?