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| ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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
$\to | A B | = a, \to | A D | = b = \to | B C |, \to | A C | = c$
$\to A B . \to A C = \to | A B | | \to A C | cos (\to A B, \to A C)$
$\Rightarrow a \times c \times \frac{a^{2} + b^{2} - c^{2}}{2 a c}$
$\Rightarrow \frac{a^{2} + b^{2} - c^{2}}{2}$

Suggest Corrections

Similar questions

In the adjoining figure, if $B C = a, A C = b, A B = c$ and $∠ C A B = 120^{\circ}$ ,
then which of the following is the correct relation?

In the adjoining figure, if BC = a, AC = b, AB = c and $∠ C A B = 120^{\circ}$ , then the correct relation is-

In the adjoining figure, if $B C = a, A C = b, A B = c$ and $∠ C A B = 120^{\circ}$ , then the correct relation is

If a + b + c = 2s, then prove the following identities

(a) s² + (s − a)² + (s − b)² + (s − c)² = a² + b² + c²

(b) a² + b² − c² + 2ab = 4s (s − c)

(d) a² − b² − c² + 2ab = 4(s − b) (s − c)

(e) (2bc + a² − b² − c²) (2bc − a² + b² + c²) = 16s (s − a) (s − b) (s − c)

(f)

If a, b, c, d are in G.p., prove that :

(i) $(a^{2} + b^{2}), (b^{2} + c^{2}), (c^{2} + d)^{2}$ are in G.P.

(ii) $(a^{2} - b^{2}), (b^{2} - c^{2}), (c^{2} - d)^{2}$ are in G.P.

(iii) $\frac{1}{a^{2} + b^{2}}, \frac{1}{b^{2} + c^{2}}, \frac{1}{c^{2} + d^{2}}$ are in G.P.

(iv) $(a^{2} + b^{2} + c^{2}), (a b + b c + c d), (b^{2} + c^{2} + d^{2})$

Join BYJU'S Learning Program

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?