Question

Solve the following
r1=3i−2j+k,r2=2i−4j−3k,r3=−i+2j+2k.Find r2.r1

5
7
8
-5

Answer 1

Answer on Question #46941, Math, Vector Calculus

Let

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

Find $r_2 \cdot (r_1 \times r_3)$

Solution

$$r _ {2} \cdot (r _ {1} \times r _ {3}) = \left( \begin{array}{ccc} r _ {2 i} & r _ {2 j} & r _ {2 k} \\ r _ {1 i} & r _ {1 j} & r _ {1 k} \\ r _ {3 i} & r _ {3 j} & r _ {3 k} \end{array} \right)$$ $$r _ {2} \cdot (r _ {1} \times r _ {3}) = \left| \begin{array}{ccc} 2 & -4 & -3 \\ 3 & -2 & 1 \\ -1 & 2 & 2 \end{array} \right| = \\ = 2 \cdot (-2) \cdot 2 + (-4) \cdot 1 \cdot (-1) + (-3) \cdot 3 \cdot 2 - (-3) \cdot (-2) \cdot (-1) - (-4) \cdot 3 \cdot 2 - 2 \cdot 1 \cdot 2 = \\ = -8 + 4 - 18 + 6 + 24 - 4 = 4$$

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