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The vector aa¯ is directed due north and |a| = 24. The vector bb¯ is directed due west and b|b¯|=7. Find ab|a¯+b¯|. - Mathematics and Statistics

Sum

The vector `bar"a"` is directed due north and |a| = 24. The vector `bar"b"` is directed due west and `|bar"b"| = 7`. Find `|bar"a" + bar"b"|`.

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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`

Concept: Vectors and Their Types
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