# Thread: Dot product with only length and angles

1. ## Dot product with only length and angles

Hi,

I have the following question:

"Find the dot product of 2 vectors if their lengths are 4 and 2/3 and the angle between them is 0.75 radians?"

I am having trouble, as most examples, the angle between them is acute - so I cannot visualize graphically how this scenario works.

Or am I over-thinking this and it is simply cos(135) x 4 x 2/3?

TIA

2. Just 4 x 2/3 x cos(0.75 rads)

Remember, the dot product is a scalar and invariant under rotation and reflection transformations. This means you can draw any two vectors that fit the description, and they should all give you the same answer.
E.g. First vector has length 4 along x-axis. Second vector has length 2/3 rotated 0.75 rads on the x-y plane. Now you can obtain the same result analytically.

3. Originally Posted by lindah
Hi,

I have the following question:

"Find the dot product of 2 vectors if their lengths are 4 and 2/3 and the angle between them is 0.75 radians?"

I am having trouble, as most examples, the angle between them is acute - so I cannot visualize graphically how this scenario works.

Or am I over-thinking this and it is simply cos(135) x 4 x 2/3?

TIA
No, it is simply cos(.75)x 4 x 2/3. Why did you change to "135" when you were given ".75"?

(135 degrees is the same as $\displaystyle .75\pi= 2.356$ radians, not .75 radians. You really should learn not to automatically change to degrees.)