How do I find the dot product of $< 2, 3 >$ $<2, 3>$ and $< 4, - 7 >$ $<4, −7>$ ?

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How do I find the dot product of $< 2, 3 >$ $<2, 3>$ and $< 4, - 7 >$ $<4, −7>$ ?

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Answer 1 · 2014-10-02T16:10:26

Let's begin by naming our vectors.

v $= < 2, 3 >$ $=<2,3>$
w $= < 4, - 7 >$ $=<4,-7>$

Find the product of the horizontal components, $i$ $i$ .
Find the product of the vertical components, $j$ $j$ .
Then add those $2$ $2$ products together.

v $\cdot$ $*$ w $= v_{i} \cdot w_{i} + v_{j} \cdot w_{j}$ $=v_i*w_i+v_j*w_j$

v $\cdot$ $*$ w $= (2) (4) + (3) (- 7)$ $=(2)(4)+(3)(-7)$

v $\cdot$ $*$ w $= 8 - 21$ $=8-21$

v $\cdot$ $*$ w $= - 13$ $=-13$

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How do I find the dot product of $< 2, 3 >$ $<2, 3>$ and $< 4, - 7 >$ $<4, −7>$ ?

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How do I find the dot product of $< 2, 3 >$ $<2, 3>$ and $< 4, - 7 >$ $<4, −7>$ ?