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Question

There are two vectors. The first one has initial and terminal points as A(–1, 3), B(2, 4) respectively. The second one has initial and terminal points as. C(1, -2), D(4, -1) respectively. The two vectors are not equal vectors.

A
True
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B
False
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Solution

The correct option is B False
First vector AB=OBOA (Using triangle law for vector addition)
= ((2 - (-1)), (4 - 3))
= (3, 1)
AB=(3)2+(1)2
=10.
Second vector CD=ODOC (Using triangle law for vector addition)
= ((4-1), (-1-(-2)))
= (3, 1)
CD=32+12
=10
So AB=CD
Now only equal magnitude doesn't make them equal vectors. They have to have the same directions as well for equality to hold.
If AB and CD have same slope, that means they have same directions.
Slope of AB=432(1)=13
Slope of CD=1(2)41=13
So their magnitude and direction are same.
So AB and CD are equal vectors.

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