Cross Products
<1,2,3> x <4,5,6>
<-3, 6, -3>
(2,4,0)
:D
Vector:
<67,19,24>
Yes! (Component/Angle Bracket Notation)
-40
Find the vector PQ given by points P: (4,9) and Q: (-2,16)
PQ = <-6,7>
<1,2,-1> x <0,3,4>
<11,-4,3>
(1,4,5)
Idk how to draw in here
Vector:
<2i,4j,9k>
No!
The dot product of <4,9,1> and <-3,3,6>
21
Find the length (magnitude) of vector <17,9>
sqrt(370)
Compute a x b:
a: 6j
b: 2i+9k
<54, 0, 12>
(-1,2,1)
art
Vector:
<9-t, 4, 7+2t>
Yes!
Find h s.t the dot product of p and q = 0.
p = 2h(i) + 3(j) + (k)
q = 4(i) + 5h(j) - 4(k)
h = 4/23
Given vector v = <-9,4>, calculate -4v
<36,-16>
Compute u x v
u: 3i-2k
v: -i+4j+k
<-8,-1,12>
(-2,-1,6)
GRAFING
Plane:
4x-3y+9z=12
Yes!
Find the projection of vector a onto vector b:
a: 2i-j+3k
b: i+4j-k
(-5/18)i (-20/18)j + (5/18)k
Given vectors q = <9,1> and r = <11,7>, calculate q-r
<-2,-6>
Given vectors r(t) = <t, t^2,1> and w(t) = <1, -t, 2>, evaluate r(2) x w(2) at t=2.
<10,-3,8>
(-3,-4,-5)
*insert math wizard graph here*
Plane:
2(x-3) + 4(y+1) - 5(z+2)
No!
Must set equal to 0!!!
Find the scalar projection of vector a onto vector b
a: <2, -1, 3>
b: <1, 4, -1>
-(5/sqrt(18))
Find a unit vector in the same direction as v = <4,8>
u = <sqrt(5)/2, 2sqrt(5)/2>