Find the True Statement About Dot Product of Two Vectors

[Tiven white]

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

 

[Tanya Sharma]

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 .

 

[szynkasz]

$$\vec{u}\circ\vec{v}=|\vec{u}|\cdot|\vec{v}|\cos\angle(\vec{u},\vec{v})=-1\Rightarrow \cos\angle(\vec{u},\vec{v})<0\Rightarrow 90^o<\angle(\vec{u},\vec{v})<270^o$$
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

 

[Tiven white]

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?

 

[Tanya Sharma]

Correct ...