Analytic Geometry Answers

Find an equation of each normal line to the curve: y = x^3 - 4x that is parallel to the line
x + 8y - 8 = 0

gent to the the line 4x-3y=6 at (3,2) and passing through (2,-1)

Let O be the origin and OA = a1i + a2j + a3k. Find the equation of the plane that contains vectors I + j + k and 2i + j + k

Let O be the origin and OA = a1i +a2j + a3k. find the equation of a line that passes through the point (1 2 3) and is perpendicular to the vector 3i+2j+3k.

Let O be the origin and OA =a1i + a2j + a3k. Find the equation of the planes such that every point on the plane is equidistant from the two end of the vector OA. You are asked to do this by first finding the point of intersection of the plane with the vector OA. State the condition for vector OA to have a magnitude iof 25

6. If
A1=3i−j−4k
A1=3i−j−4k
,
A2=−2i+4j−3k
A2=−2i+4j−3k
,
A3=i+2j−k
A3=i+2j−k
, find
|3A1−2A3+4A3|
7 Find a unit vector parallel to the resultant vector
A1=2i+4j−5k
A1=2i+4j−5k
,
A2=1+2j+3k
8 Given the scalar defined by
ϕ(x,y,z)=3x2z−xy2+5
ϕ(x,y,z)=3x2z−xy2+5
,find
ϕ
ϕ
at the points (-1,-2,-3)
9 The following forces act on a particle P:
F1=2i+3j−5k
F1=2i+3j−5k
,
F2=−5i+j+3k
F2=−5i+j+3k
,
F3=i−2j+4k
F3=i−2j+4k
,
F4=4i−3j−2k
F4=4i−3j−2k

, Find the magnitude of the resultant
10. If a and b are non-collinear vectors and
A=(x+y)a+(2x+y+1)b

1 Find the magnitude of vector
A=3i−2j+2k
Given that
A1=3i−2j+k
A1=3i−2j+k
,
A2=2i−4j−3k
A2=2i−4j−3k
,
A3=−i+2j+2k
A3=−i+2j+2k
, find the magnitudes of
2A1−3A2−5A3

3 Given that
A1=2i−j+k
A1=2i−j+k
,
A2=i+3j−2k
A2=i+3j−2k
,
A3=3i+2j+5k
A3=3i+2j+5k
and
A4=3i+2j+5k
A4=3i+2j+5k

,Find scalars a, b, c such that
A4=aA1+bA2+cA3

4 Let a and b be vectors, then
a×b=absinθ
a×b=absin⁡θ
is the €¦ €¦ €¦product
5 A car travels 3km due north, then 5km northeast. Determine the resultant displacement

the terminal side lies in the third quadrant and is perpendicular to the line 3x + 5y = 0?

1. find a unit vector parallel to the resultant vector A1 =2i+4j-5k, A2 = 1+2j+3k
2.given the scaler defind by phi(x,y,z)=3x^2z-xy^2+5. find phi at the points (-1,-2,-3)

if a circle of radius 5 was centred on the point C(3,8), if two points on the edge are A(6,4) and B(-1,11): prove that both A and B are points on the edge of the circle