Analytic Geometry Answers

Suppose u and v are non zero factors in 3-space, where u=(u1,u2,u3) and v=(v1,v2,v3).

Prove that u * v is perpendicular to both u and v by making use of the det product.

Please assist.

Find the angle between the vectors
α
Ì
…
=
2
i
+
2
j
−
k
αÌ…=2i+2j−k and
\
e
t
a
=
6
i
−
3
j
+
2
k
\eta=6i−3j+2k.

Pls Help *MTH282*
Suppose the position vector of X and Y are (1,2,4) and (2,3,5), find the position vector of a point Z that bisect XY in the ratio 2:3
A 7i+12j+22k
B. 7i-12j+22k
C.frac{1}{7} (7i+12j+22k)
D.frac{1}{17} (7i-12j+22k)

v1(3,-2,-2), v2(2,-1,-2), v3(-1,1,1) , u(0,1,h)
find all values of h such that u is a linear combination of v1, v2 and v3

Suppose the position vector of X and Y are (1,2,4) and (2,3,5), find the position vector of a point Z that bisect XY in the ratio 2:3.

a.\\(7i+12j+22k\\)
b.\\(7i-12j+22k\\)
c.\\(\\frac{1}{7} (7i+12j+22k)\\)
d.\\(\\frac{1}{17} (7i-12j+22k)\\)

The quantity αdot (\eta times gamma)is called the ____

a.scalar-vector triple product
b.scalar-vector product
c.vector triple product
d.scalar triple product

Determine the value of a, so that If α=2i+aj+k and \eta=4i−j−2k are perpendicular.

a.2
b.5
c.4
d.3

Vectors with same direction (parallel), opposite sense but different magnitude are called


a.unlike vectors
b.like vectors
c.unit vectors
d.equal vectors