## anonymous one year ago Find a • b. a = 4i + 8j, b = -2i + 3j

1. welshfella

this is the 'dot' product of 2 vectors a . b = 4i*-2i + 8j*3j

2. welshfella

its also called the Scalar product

3. welshfella

can you simplify this further?

4. welshfella

the square of the unit vectors i and j both = 1

5. anonymous

Okay. hmm

6. anonymous

-8,24

7. anonymous

@welshfella

8. Empty

@xamr Almost, but the dot product gives you a single value not a pair of values. So you need to ad those two numbers together. One application of the dot product is to calculate length which is the square root of the dot product, $$\text{length of vector a} = \sqrt{\vec a \cdot \vec a }$$

9. anonymous

So 16

10. Empty

Yep

11. welshfella

yes

12. Jhannybean

By thinking of i,j,k as components x,y,z we can rewrite vectors a and b. $\vec a = \langle 4~,~8\rangle ~,~ \vec b = \langle -2~,~ 3\rangle$

13. anonymous

Thank you all.

14. welshfella

yw

15. Empty

when you dot a vector with another vector, you get the amount of projection of one vector onto another. So if two vectors are at right angles to each other, then there's no projection at all, and the dot product is zero $$\vec a \cdot \vec b = 0$$ means they're perpendicular to each other

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