In a parallelogram ABCD- -AB-a- -AD-b and -AC-c- then which of the following is-are CORRECT-

The correct option is A AB.AC=a^2 + b^2 c^22 .Consider a parllelogram ABCD, #160; Here AD is parallel to BC |⃗A⃗B⃗|⃗=a,|⃗A⃗D⃗|⃗=b=|⃗B⃗C⃗|⃗,|⃗A⃗C⃗| ...

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Standard XII

Mathematics

Parabola

In a parallel...

Question

In a parallelogram ABCD, $| - - \to A B | = a$ , $| - - \to A D | = b$ and $| - - \to A C | = c$ . then which of the following is/are CORRECT?

- - \to A B . - - \to A C = \frac{a^{2} + b^{2} - c^{2}}{2}

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- - \to A B . - - \to A C = \frac{b^{2} + c^{2} - a^{2}}{3}

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- - \to A B . - - \to A C = \frac{3 a^{2} + b^{2} - c^{2}}{2}

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- - \to A B . - - \to A C = \frac{c^{2} - a^{2} - b^{2}}{2}

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Solution

The correct option is A $- - \to A B . - - \to A C = \frac{a^{2} + b^{2} - c^{2}}{2}$ .
Consider a parllelogram ABCD, Here AD is parallel to BC
$\to | A B | = a, \to | A D | = b = \to | B C |, \to | A C | = c$
$\to A B . \to A C = \to | A B | | \to A C | cos (\to A B, \to A C)$
$\Rightarrow a \times c \times \frac{a^{2} + b^{2} - c^{2}}{2 a c}$
$\Rightarrow \frac{a^{2} + b^{2} - c^{2}}{2}$

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In a parallelogram ABCD, |−−→AB|=a,|−−→AD|=b and |−−→AC|=c. then which of the following is/are CORRECT?

The correct option is A −−→AB.−−→AC=a2+b2−c22.Consider a parllelogram ABCD, Here AD is parallel to BC→|AB|=a,→|AD|=b=→|BC|,→|AC|=c→AB.→AC=→|AB||→AC|cos(→AB,→AC)⇒a×c×a2+b2−c22ac⇒a2+b2−c22

In a parallelogram ABCD, $| - - \to A B | = a$ , $| - - \to A D | = b$ and $| - - \to A C | = c$ . then which of the following is/are CORRECT?