Question

If (A cap + B cap = C cap)then find the value of (A cap -B cap=?)​

Answer 1

value of |A - B| = √{2(A² + B²) - C²}

it is given that ( A + B ) = C

we have to find the value of |(A - B)|

A + B = C

⇒|A + B| = |C|

⇒√{A² + B² + 2ABcosθ} = |C|

⇒A² + B² + 2ABcosθ = C²

⇒cosθ = (C² - A² - B²)/2AB.........(1)

|A - B| = √{A² + B² - 2ABcosθ}

= √{A² + B² - 2AB × (C² - A² - B²)/2AB}

= √{A² + B² - (C² - A² - B²)}

= √{2(A² + B²) - C²}

therefore, |A - B| = √{2(A² + B²) - C²}

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Answer 2

Answer:

|A - B| = √{2(A² + B²) - C²}

Step-by-step explanation:

value of |A - B| = √{2(A² + B²) - C²}

it is given that ( A + B ) = C

we have to find the value of |(A - B)|

A + B = C

⇒|A + B| = |C|

⇒√{A² + B² + 2ABcos0} = |C|

⇒A² + B² + 2AB cos0 = C²

⇒cosθ = (C² - A² - B²)/2AB     (1)

|A - B| = √{A² + B² - 2AB cos0}

= √{A² + B² - 2AB × (C² - A² - B²)/2AB}

= √{A² + B² - (C² - A² - B²)}

= √{2(A² + B²) - C²}

therefore, |A - B| = √{2(A² + B²) - C²}