Analytic Geometry Answers

____ vector with reference to a point X to origin O is the vector
OX used to specify the true position of X with respect to O.
a.Location
b.Positive
c.Negative
d.Position

A vector whose magnitude is unit is called ____
a.equal vectors
b.unlike vectors
c.unit vectors
d.like vectors

____ is any quantity that has both a magnitude and a direction.
a.None of the above
b.Vector and scalar quantity
c.Vector quantity
d.Scalar quantity

Suppose that the coordinates of R be (3,4,12), what is (OR) ƒ—?
a.3i-4j+12k
b.3i+4j-12k
c.3i-4j-12k
d.3i+4j+12k

Suppose that the coordinates of R be (3,4,12), what are the direction cosines of
(OR) ƒ—?
a.\\(\\frac{3}{14}, \\frac{4}{14}, \\frac{12}{14}\\)
b.\\(\\frac{1}{13}, \\frac{4}{13}, \\frac{11}{13}\\)
c.\\(\\frac{1}{14}, \\frac{4}{14}, \\frac{11}{14}\\)
d.\\(\\frac{3}{13}, \\frac{4}{13}, \\frac{12}{13}\\)

If vector x * vector b = vector c * vector b and vector x . vector c =0 then find vector x

Given that z = 1 + i√2, express in the form a + ib each of the complex numbers
p = z + 1/z, q = z − 1/z. In an Argand diagram, P and Q are the points which
represent p and q respectively, O is the orgin, M is the midpoint of P Q and G is the
point on OM such that OG = 2
3
OM. Prove that angle P GQ is a right angle

(a) Find the real root of the equation z3 + z + 10 = 0 given that one root is 1 − 2i.
(b) Given that 3 + i is a root of the equation z3 − 3z2 − 8z + 30 = 0, find the
remaining roots.
(c) Given that 1 + i is a root of the equation z3 − 2z + k = 0, find the other two
roots and the value of the real constant k.
(d) Given that 2 − 3i is a root of the equation z3 + pz2 + qz + 13 = 0, find the other
two roots and the values of the real constants p and q.
(e) Show that z = i is a root of the equation z4 + z3 + z − 1 = 0. Find the three
other roots.

6.Vectors with same direction, same a sense (same arrow) but different magnitude are called____
unlike vectors
unit vectors
equal vectors
like vectors

4.Suppose that α=2i−3j+k and \eta=7i−5j+k , find a unit vector perpendicular to α
and \(\eta) respectively.
\\(\\frac{-2i+5j+11k }{5\\sqrt(6)}\\)
\\(\\frac{2i-5j+11k }{5\\sqrt(6)}\\)
\\(\\frac{2i+5j-11k }{5\\sqrt(6)}\\)
\\(\\frac{2i+5j+11k }{5\\sqrt(6)}\\)