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91Ó°ÊÓ

Evaluate the dot product A⇶Ä.B⇶Ä,if

a. A⇶Ä=3i^+4j^and B⇶Ä=2i^-6j^

b.A⇶Ä=3i^-2j^andB⇶Ä=6i^+4j^

Short Answer

Expert verified

a. A⇶Ä.B⇶Ä=-18

b.A⇶Ä.B⇶Ä=10

Step by step solution

01

Given information (Part a)

A⇶Ä=3i^+4j^

B⇶Ä=2i^-6j^

02

Dot product (part a)

A⇶Ä.B⇶Ä=(3i^+4j^).(2i^-6j^)A⇶Ä.B⇶Ä=(3×2)+(4×(-6))A⇶Ä.B⇶Ä=6-24=-18

03

Given information (Part b)

A⇶Ä=3i^-2j^

B⇶Ä=6i^+4j^

04

Dot product (part b)

A⇶Ä.B⇶Ä=(3i^-2j^).(6i^+4j^)A⇶Ä.B⇶Ä=(3×6)+((-2)×4)A⇶Ä.B⇶Ä=18-8=10

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