# Dot product

## Homework Statement

The dot product of.two vectors is -1which of the following statements is true

A. They must be unit vectors pointing in opposite directions.
B. They must be unit vectors pointing j. The same direction.
C. They must be more than 90( and less than 270 )degrees from each other.
D. They must be perpendicular to each other.
E. They must sum to zero

## Homework Equations

I have eliminated D though I find the others difficult

## The Attempt at a Solution

A.B = |A||B|cosθ .So we are looking at the product of three quantities whose product is -1 .Two quantities are magnitudes ,hence positive.Now only cosθ term can be negative .

Now rethink about the options .A few of them can be eliminated .

$$\vec{u}\circ\vec{v}=|\vec{u}|\cdot|\vec{v}|\cos\angle(\vec{u},\vec{v})=-1\Rightarrow \cos\angle(\vec{u},\vec{v})<0\Rightarrow 90^o<\angle(\vec{u},\vec{v})<270^o$$
the same direction: $$\cos\angle(\vec{u},\vec{v})=\cos 0^o=1\Rightarrow \vec{u}\circ\vec{v}\ge 0>-1$$ so not B

$$2i\circ\left(-\frac{1}{2}i\right)=-1$$
so not A nor E

A.B = |A||B|cosθ .So we are looking at the product of three quantities whose product is -1 .Two quantities are magnitudes ,hence positive.Now only cosθ term can be negative .

Now rethink about the options .A few of them can be eliminated .

Ok so in order to obtain a negative value the value of the angle would have to be between 90 and 270 then this leaves option ' c' is that so?

Correct ...