about vectors nd their formulas
Answers
Answer:
Apply analytical methods of vector algebra to find resultant vectors and to solve vector equations for unknown vectors.
Interpret physical situations in terms of vector expressions.
Vectors can be added together and multiplied by scalars. Vector addition is associative ((Figure)) and commutative ((Figure)), and vector multiplication by a sum of scalars is distributive ((Figure)). Also, scalar multiplication by a sum of vectors is distributive:
α
(
→
A
+
→
B
)
=
α
→
A
+
α
→
B
.
In this equation,
α
is any number (a scalar). For example, a vector antiparallel to vector
→
A
=
A
x
^
i
+
A
y
^
j
+
A
z
^
k
can be expressed simply by multiplying
→
A
by the scalar
α
=
−
1
:
−
→
A
=
−
A
x
^
i
−
A
y
^
j
−
A
z
^
k
.
EXAMPLE
Direction of Motion
In a Cartesian coordinate system where
^
i
denotes geographic east,
^
j
denotes geographic north, and
^
k
denotes altitude above sea level, a military convoy advances its position through unknown territory with velocity
→
v
=
(
4.0
^
i
+
3.0
^
j
+
0.1
^
k
)
km
/
h
. If the convoy had to retreat, in what geographic direction would it be moving?
Solution
Show Answer
Answer:
Vectors are quantities that represent both directions and velocities..
Explanation:
Formulas are :-
The vector equation of a line passing through the point a and in the direction d is:
r = a + td , where t varies.