H2 Maths: Vectors

J2011

13 Jan 11, 22:35

Need help: n = (a1, a2, a3) x (b1, b2, b3) = ?

Thanks.

wee_ws

14 Jan 11, 06:36

Hi,

This is straightforward. Please refer to your notes. Thanks.

Cheers,
Wen Shih

J2011

14 Jan 11, 21:50

Hi Sir,

Thanks for the information. I'm a self-study parent hope to grow together with my school kid . Anyway have just got the answer online. Thanks.

$\mathbf{a}\times\mathbf{b}= \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ \end{vmatrix}.$

$\mathbf{a}\times\mathbf{b}= \begin{vmatrix} a_2 & a_3\\ b_2 & b_3 \end{vmatrix} \mathbf{i} - \begin{vmatrix} a_1 & a_3\\ b_1 & b_3 \end{vmatrix} \mathbf{j}+ \begin{vmatrix} a_1 & a_2\\ b_1 & b_2 \end{vmatrix} \mathbf{k}$

wee_ws

15 Jan 11, 07:41

Hi,

That is great! You may refer to my learning resources at

wenshih.wordpress.com or weews.webs.com

Jiayou!

Cheers,
Wen Shih

wee_ws

15 Jan 11, 07:44

Hi,

The vector n is the normal to the plane.

The vector product can also applied to find the area of a triangle.

Thanks.

Cheers,
Wen Shih

J2011

19 Jan 11, 11:12

Hi, when we prove that vector AB = vector CD, then ABCD is a parallelogram. Why can't it be a rectagle or a square?

Thanks.

eagle

19 Jan 11, 11:53

Hi,

a square and a rectangle are both subsets of parallelogram. They require AB to be perpendicular to BC, or CD to be perpendicular to AD. For a square, AB must be of the same magnitude as BC since all 4 sides are equal.

When Vector AB = vector CD, it just means
1) AB is in the same direction as CD
2) AB has the same magnitude as CD

At the same time, when AB = CD, BC = AD

Hence, we proved it is a parallelogram. However, in no way did we prove that AB is perpendicular to BC. If it does, we can consider it a rectangle.

J2011

19 Jan 11, 20:43

Thanks eagle for the detail explanation.

wee_ws

19 Jan 11, 22:47

Hi J2011,

This aspect of geometry has been covered at O-level. It is always useful to try to relate H2 Maths with O-level content :)

The following points should be committed to memory:

1. All parallelograms are quadrilaterals. Only some quadrilaterals are parallelograms.

2. All rectangles and squares are parallelograms. Only some parallelograms are rectangles and squares.

3. All squares are rhombuses. Only some rhombuses are squares.

4. All rhombuses are kites. Only some kites are rhombuses.

Thanks.

Cheers,
Wen Shih

J2011

20 Jan 11, 08:52

Hi Mr Wee, noted with thanks.