If -x y z p q r a b c- then 2x-4p p-6a a 2y-4q q-6b b 2z-4r r-6c c is equal to

If $Δ$ is an operation, such that for integers a and b. We have $a Δ b = a \times b - 2 \times a \times b + b \times b (- a) \times b + b \times b,$ then find
$4 Δ (- 3)$
Also, show that $4 Δ (- 3) \neq (- 3) Δ 4$

Q. If

D

be the middle point of the side

B C

△ A B C

whose area is

Δ

and

∠ A D B = θ

, then prove

\frac{{A C}^{2} - {A B}^{2}}{4 Δ} = cot θ

Join BYJU'S Learning Program

If Δ=∣∣ ∣∣xyzpqrabc∣∣ ∣∣, then ∣∣ ∣∣2x+4pp+6aa2y+4qq+6bb2z+4rr+6cc∣∣ ∣∣ is equal to

The correct option is A 2Δ∣∣ ∣∣2x+4pp+6aa2y+4qq+6bb2z+4rr+6cc∣∣ ∣∣C2→C2−6C3;C1→C1−4C2∣∣ ∣∣2xpa2yqb2zrc∣∣ ∣∣=2∣∣ ∣∣xpayqbzrc∣∣ ∣∣=2ΔAns: A

If $Δ = ∣ ∣ ∣ ∣ \begin{matrix} x & y & z p & q & r a & b & c \end{matrix} ∣ ∣ ∣ ∣$ , then $∣ ∣ ∣ ∣ \begin{matrix} 2 x + 4 p & p + 6 a & a 2 y + 4 q & q + 6 b & b 2 z + 4 r & r + 6 c & c \end{matrix} ∣ ∣ ∣ ∣$ is equal to