H2 Maths: Vectors

J2011 SG

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

Thanks.

wee_ws SG

Hi,

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

Cheers,
Wen Shih

J2011 SG

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 SG

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 SG

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 SG

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 SG

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 SG

Thanks eagle for the detail explanation.

wee_ws SG

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 SG

Hi Mr Wee, noted with thanks.