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Question
The vector `bar"a"` is directed due north and `|bar"a"|` = 24. The vector `bar"b"` is directed due west and `|bar"b"| = 7`. Find `|bar"a" + bar"b"|`.
Solution
Let `bar"AB" = bar"a", bar"BC" = bar"b"`
Then `bar"AC" = bar"AB" + bar"BC" = bar"a" + bar"b"`
Given: `|bar"a"| = |bar"AB"|`
= `l("AB")`
= 24
and
`|bar"b"| = |bar"BC"|`
= `l("BC")`
= 7
∵ ∠ABC = 90°
∴ `["l"("AC")]^2 = ["l"("AB")]^2 + ["l"(BC)]^2`
`= (24)^2 + (7)^2`
= 625
∴ |l(AC)| = 25
∴ `|bar"AC"| = 25`
∴ `|bar"a" + bar"b"| = |bar"AC"| = 25`
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