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Question
If `|vec"A" xx vec"B"| = sqrt3 vec"A" . vec"B"` then the value of is `|vec"A" xx vec"B"|` is
Options
`sqrt("A"^2 + "B"^2 + "AB")`
`sqrt("A"^2 + "B"^2 + 1/2 "AB")`
`sqrt("A"^2 + "B"^2 + 1/sqrt3 "AB")`
`sqrt("A"^2 + "B"^2 + sqrt3 "AB")`
MCQ
Solution
`sqrt("A"^2 + "B"^2 + "AB")`
Explanation:
`|vec"A" xx vec"B"| = sqrt3 (vec"A" . vec"B")`
AB sin q = `sqrt3 "AB" cos "q"`
⇒ tan q = `sqrt3` ∴ q = 60°
Now `|vec"R"| = |vec"A" xx vec"B"|= sqrt("A"^2 + "B"^2 + 2"AB" cos θ)`
= `sqrt("A"^2 + "B"^2 + 2"AB" (1/2))`
= `sqrt("A"^2 + "B"^2 + "AB")`
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