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Question
If `|bara|` = 3, `|barb|` = 5, `|barc|` = 7 and `bara + barb + barc = bar0`, then the angle between `bara` and `barb` is ______.
Options
`π/2`
`π/3`
`π/4`
`π/6`
Solution
If `|bara|` = 3, `|barb|` = 5, `|barc|` = 7 and `bara + barb + barc = bar0`, then the angle between `bara` and `barb` is `underlinebb(π/3)`.
Explanation:
Given `bara + barb + barc = bar0`,
`|bara|` = 3, `|barb|` = 5, `|barc|` = 7
`\implies (bara + barb).(bara + barb) = (-barc).(-barc)`
`\implies` |a|2 + |b|2 + 2|a||b| cos θ = |c|2
`\implies` 9 + 25 + 30 cos θ = 49
`\implies` cos θ = `1/2`
∴ Angle between `bara` and `barb` is `π/3`
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