MECHANICS

VECTORS OR CROSS PRODUCT ON TWO OR THREE DIMENSION, CROSS PRODUCT OF TWO VECTORS AND APPLICATION OF CROSS PRODUCT

Vector Product of two vectors

Given two vectors and whose directions are inclined at an angletheir vector productis defined as a vector whose magnitude is sin and whose directions is perpendicular to both and  and also being positive relative to a rotation from themvector  and also being positive relative to a rotation from the vector to the re

ctor .

            The vector product of and b is designated

GENERAL EVALUATION

1) Find the vector product of  a= 4i -3j +4k and  b = -I + 2j +7k

2) Given that p = 7i + 2j + k  and q = 3i – 2j + 4k find ; (i) p x q  (ii) | p x q | (iii) the unit vector perpendicular to both p and q

3) Find the sine of the angle between the vectors :  a = I – j + k  and  b = 8i + 2j + 3k

4) The adjacent sides of a parallelogram  are PQ= 4i + 3j + k  and PR = -5i + 2j +3k find the area of the parallelogram

5) The position vectors OA, OB and OC are  2i – 3j + 4k , 6i + 4j -8k and 3i + 2j + 5k respectively  find  (i) vector AB  (ii) vector BA  (iii) vector BC (iv)  AB x BC

Reading Assignment: New Further Maths Project 2 page 216 – 222

 

WEEKEND ASSIGNMENT

Given that  a = I + 2j + k  and   b = 2i +3j- 5k

1) find ( a x b ) . a    a)  0  b) 1  c) 2  d) 3

2) find ( a x b ) . b     a) 1  b) 2  c) 0  d) 3

Given that  p = I + 5j + 6k    and q = – 2i + j + 3k

3)  find p x q    a) 15i +11j -11k  b) 11i – 15j + 11k   c)  11i – 11j + 15k  d) 11i- 15j -11k

4) find q x p    a)  -11i  + 15j – 11k  b) 11i –  15j + 11k    c) 15i – 11j-11k  d)  15i+11j+11k

5) Given that  a = i – j+ 3k  and   b = 6i + 2j – 2k     find   ( a + b ) . ( a x b )     a)  1  b) 0   c) 2  d) 3

THEORY

1)  AB = 4i +3j+5k  and AC= 2i-3j+k  are two sides of a triangle  ABC , find the area of the triangle

2) PQ = 2i+5j+3k  and  PR = 3i-3j + k  are two adjacent sides  of  a parallelogram, find the area of the parallelogram.

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