Analytic Geometry Answers

____ 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)}\\)

Suppose u; v and w are vectors in 3 space, where u = (u1;u2; u3) ; v = (v1; v2; v3) and w = (w1;w2;w3) :

Express (u x v) x w as a determinant

If v∈R2 lies in the first quadrant and makes an angle π/4 with the positive x-axis and ||v||=2, then, Select one:



a. v=⟨2√2, 2√2⟩



b. v=⟨2, 2√3⟩



c. v=⟨√2, √2⟩



d. v=⟨2, −2√3⟩



e. v=⟨2√2, −√2⟩