Hi,
Why don't you draw them out on paper to enable
visualisation?
The topic of vectors in H2 Maths can be quickly
summarised into these 8 points:
1. Collinearity of 3 points and Ratio Theorem.
2. Definition of the scalar product,
i.e. a .
b = |a| |b| cos
\theta.
This definition is useful for finding length of projection
of one vector onto another, angle between 2 vectors, angle between
2 lines, angle between 2 planes and angle between line and
plane.
3. Definition of the magnitude of the vector
product,
i.e. |a x
b| = |a| |b| sin
\theta.
This definition is useful for finding shortest distance
between point and line as well as areas of figures.
4. The normal c is parallel to
a x b means that
c is perpendicular to each of a
and of b. This idea is extremely helpful for
finding equation of a plane containing a line and is parallel to
some vector. It is also useful to understand the line of
intersection between two planes.
5. The relationship between two lines may be
intersecting, parallel or skew.
6. The relationship between three planes may be
intersecting at a point, intersecting at a line, parallel or
non-intersecting.
7. The relationship between a line and a plane may be
intersecting, parallel or containment (i.e. line is on the
plane).
8. Equation of a line may be expressed in vector,
parametric or cartesian forms. Equation of a plane may be expressed
in vector, scalar product or cartesian forms.
Thanks!
Cheers,
Wen Shih
Hi Wee_ws,
Thanks for the very useful summary on the topic Vector.
However, I have difficulties to understand the topic Vector.
1. What does Dot/Scalar Product a.b = lal.lbl.cos
theta mean (textbook just gives us the formula and the diagram and
it does not explain why a.b will be equal to lal.lbl.cos theta and
it also does not explain the meaning of a.b or lal.lbl.cos
theta ?
2. What does cross product of vectors la x bl =
lal.lbl.sin theta mean (the textbook does not explain why la xbl
will be equal to lal.lbl.sin theta and it also does not explain why
the multiplication of the two vectors a and b on the horizontal
plane will lead to the third vector on the vertical plane ? The
textbook also did not explain a normal vector, it just says that
for a plane parallel to vectors b and vector c, the vector b
x c will be the normal vector to the plane ie why the normal vector
is b x c.
3. Based on the diagram in the textbook, it is difficult to
visualise the 3 components of a vector, it will be good if there is
a software that will allow us to visual it in 3D with motion
function ie it can be rotated. It will be so much easier to
understand the H2 maths vector topic especially on those
parts involving planes and lines.
Thanks for the very useful summary and help.