Question

Compute u × v where u = (1, 2, 3) and v = (1, 1, 2).

Answer 1

ok

Answer 2

2*2-1*3)i-(1*2-1*3)j+1*1-1*2)k

Answer 3

so 1i+1j-1k

Answer 4

wait is there are formula when did you do 2*2 first

Answer 5

you need to understand determinants first which always pops up when you do cross products.

Answer 6

yes i know that but what are the steps u are using

Answer 7

http://www.mathsisfun.com/algebra/matrix-determinant.html

It's tricky to explain directly but you pick the i element, then cross out then row and column with it (think Sudoku elimination) then find the determinant of the remaining 2x2 matrix, do the same for element j and k. Signs interchange however so you have

i det1 - j det 2 + k det 3.

Answer 8

I dont get how the middle one is plus 1 it should be negative 1 right ? since you did 1*2-1*3

Answer 9

which would be 2-3=-1

Answer 10

oh wait cuz its the rule always do + then - then + right?

Answer 11

yeah + - + etc. it alternates

Answer 12

Find a vector equation of the line passing through P(3, −1, 4) and perpendicular to
the plane 3x − 2y − z = 0.

Answer 13

can u help me with this one

Answer 14

A normal vector to the plane of the form ax + by + cz = d is (a, b, c)
So for 3x - 2y - z = 0 a normal vector is (3,-2,-1)

You just need your line to be parallel to this normal vector and passing through the point P

In general we write Q(v) = P(v) + A(v) t where P(v) is the vector pt Q passes through and A(v) is your parallel vector to Q(v) and t is your parameter.

Answer 15

Find the equations of the line of intersection of the planes 3x + y − 2z = 1 and
x + y + z = 5.

Answer 16

can you help me with one too

Answer 17

a line is a point and a direction vector

Answer 18

since the point is on both plane 1 and plane 2, you can solve the system of equations for a particular solution

Answer 19

(0, 7/3,4/3) is a good one, you can verify that this does satisfy both of the euqations

Answer 20

y is 11/3, sorry

Answer 21

the direction vector is perpendicular to the normal of plane 1 and 2

Answer 22

therefore it is the cross of the two normals

Answer 23

(3,1,-2)x(1,1,1)=(3,-5,2)

Answer 24

answer is (0,11/3,4/3)+(3,-5,2)*t