Question

Given vector u=3i + 5j and v=6i - 2j, find 3u + 2v and the dot product of u and v.

Answer 1

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Answer:

• 3u+2v = 21i +11j
• u·v = 8

Step-by-step explanation:

The desired sum is ...

  3u +2v = 3(3i +5j) +2(6i -2j) = (3·3 +2·6)i +(3·5+2(-2))j = 21i +11j

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The dot product is the sum of products of corresponding component values.

  u·v = (3)(6) +(5)(-2) = 18 -10 = 8