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The diagram shows OA = a and OB = b
a) Write AB in terms of a and b.
Simplify your answer.
Note: Ignore arrows above vectors eg write AB, not AB
b
-a+b
B
b) The point B divides AC in the ratio 2 : 3.
Work out vector OOin terms of a and b.
Simplify your answering

The diagram shows OA a and OB b a Write AB in terms of a and b Simplify your answer Note Ignore arrows above vectors eg write AB not AB b ab B b The point B di class=

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Answer:

OC=-3/2a+5/2b (it should be correct, sorry if it isn't)

Step-by-step explanation:

OC=OA+AB+BC

OC=a-a+b-3/2a+3/2b

OC=5/2b-3/2a

or

OC=-3/2a+5/2b

From the diagram shown, the vectors AB and OC in terms of a and b are gotten as;

A) Vector AB = b - a

B) OC = ¹/₂(5b - 3a)

  • A) We are told that;

Vector OA = a

Vector OB = b

We want to find Vector AB.

The triangle law of vector addition states that when two vectors are represented as two sides of a triangle with the order of magnitude and direction given, then the third side of that same triangle denotes the resultant vector in magnitude and direction.

Applying this to our question, we can see that vector OB has a counterclockwise direction while vector OA has a clockwise direction.

What this means is that;

Vector AB = OB - OA

Vector AB = b - a

B) We are told that point B divides AC in the ratio 2 : 3.

This means that;

BC/AB = 3/2

BC = 3(b - a)/2

Thus;

AC = AB + BC

AC = b - a + 3(b - a)/2

AC = b - a + 3b/2 - 3a/2

AC = 5b/2 - 5a/2

AC = ⁵/₂(b - a)

Applying the same law of vector addition, we can say that;

OC = AC - AO

OC = ⁵/₂(b - a) - (-a)

I used -a for AO because it is the opposite of give OA.

Thus;

OC = 5b/2 - 5a/2 + a

OC = (⁵/₂)b - (³/₂)a

OC = ¹/₂(5b - 3a)

Read more at; https://brainly.com/question/12854106

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