Question

Vectors a,b,c,d and e are drawn on a isometric grid . write each of the vectors c,d and e in terms of a and / or b . give each awnser in its simplist form

Answer 1

C = 3A

D = A + B

E = A - B

Explanation:

Answer 2

`c= 3a`

`d= b+a`

`e= a-b`

Explanation:

Given

See attachment

Required

Find c, d and e in terms of a and/or b

To answer this question, we consider the magnitude (size) and direction (positive or negative) of each vector

Up and Right direction are treated as positive

Down and Left direction are treated as negative

Solving (a): Vector c

Vector c and vector a, point towards the same direction

And the magnitude of c is such that, it can take 3 of a.

So:

`c = a + a + a`

`c =3a`

Solving (b): Vector d

This is best answered using an attachment (see attachment 2 for new positions of vector a and b)

From the new positions of a and b, we can see that:

(a): Vector b starts from the tip of d

(a): Vector a starts from the end of vector b

a, b and d all point toward the same direction (right or up)

Hence:

`d = b + a`

Solving (c): Vector e

This is best answered using an attachment (see attachment 2 for new positions of vector a and b)

From the new positions of a and b, we can see that:

(a): Vector a starts from the tip of e

(a): Vector b starts from the end of vector a

However, b points to the opposite direction of e

Hence:

`e = a - b`