Question

Given that :
r−1=6i−8j+2k,r2=4i+5j+7k,r3=−2i+j+6k is a vector.Find r1 r2

30
26
-26
19

Answer 1

Answer on Question #46815 – Math – Vector Calculus

Given that:

$$r _ {1} = 6 i - 8 j + 2 k, r _ {2} = 4 i + 5 j + 7 k, r _ {3} = - 2 i + j + 6 k$$

Find $(r_1, r_2)$.

Solution

The scalar (or dot) product $(r_1, r_2)$ of vectors

$$r _ {1} = a _ {1} i + a _ {2} j + a _ {3} k, r _ {2} = b _ {1} i + b _ {2} j + b _ {3} k,$$

can be computed by the following formula:

$$\left(r _ {1}, r _ {2}\right) = a _ {1} b _ {1} + a _ {2} b _ {2} + a _ {3} b _ {3}.$$

In our case

$$r _ {1} = 6 i - 8 j + 2 k, r _ {2} = 4 i + 5 j + 7 k$$

and so

$$\left(r _ {1}, r _ {2}\right) = 6 \cdot 4 + (- 8) \cdot 5 + 2 \cdot 7 = 24 - 40 + 14 = -2.$$

Answer: -2.

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