Analytic Geometry Answers

Determine \\(a-b-c\\), if \\(a=5i-2j\\), \\(b=3i+3j\\) and \\(c=4i-j\\)

Find in degrees the numeric value of the acute angle of rotation that eliminates the product term from the equation

7

x

2

+

24

x

y

−

34

x

+

24

y

−

185

=

0

Is there a sphere passing through (4,0,1),(10,-4,9),(-5,6,-11)and (1,2,3)?If so,find its equation.

Find the centre and radius of the sphere passing through (1,0,0),(0,1,0),(0,0,1) and (1/√3,1/√3,1/√3)?

If r = x

y

1

1 0 g

and A = 0 1 f

g f c

show that r^T Ar = 0 is the equation of the

circle in R^2 with centre (−g, −f) and radius square root(g^2 + f^2 − c).

Determine the sum of vectors \\(\\bar{CD}+\\bar{DA}\\)

If α=3i−j+2k, , β=2i+j−k and γÌ…=i−2j+2k, find α×β×γ.

a.24i+7j-5k

b.-24i+7j-5k

c.24i+7j+5k

d.24i-7j-5k

Given α=i+2j+3k, β=2i+j−k find α×β

a.5i+7j-3k

b.-5i+7j-3k

c.-5i+7j+3k

d.-5i-7j-3k

____ 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