A , B, C and D, are four points in a plane with position vectors a,b, c and d respectively such that (a-d).(b-c)=(b-d).(c-a)=0 The point D, then, is the... of the Δ ABC.

Question

A , B, C and D, are four points in a plane with position vectors a,b, c and d respectively such that (a-d).(b-c)=(b-d).(c-a)=0 The point D, then, is the... of the Δ ABC. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(a-d)⋅ (b-c)=(b-d) ⋅ (c-a)=0 ⇒ AD perp BC and BD perp CA which clearly represents from figure that D is orthocentre of Δ ABC

Q. $A, B, C$ and $D$ , are four points in a plane with position vectors $a, b, c$ and $d$ respectively such that $(a - d) . (b - c) = (b - d) . (c - a) = 0$ The point $D$ , then, is the... of the $Δ A BC$ .

$(a - d) \cdot (b - c) = (b - d) \cdot (c - a) = 0$
$\Rightarrow A D ⊥ BC$ and $B D ⊥ C A$
which clearly represents from figure that $D$ is
orthocentre of $Δ A BC$

Q. A,B,C and D, are four points in a plane with position vectors a,b,c and d respectively such that (a−d).(b−c)=(b−d).(c−a)=0 The point D, then, is the... of the ΔABC.

(a−d)⋅(b−c)=(b−d)⋅(c−a)=0 ⇒AD⊥BC and BD⊥CA which clearly represents from figure that D is orthocentre of ΔABC

Q. $A, B, C$ and $D$ , are four points in a plane with position vectors $a, b, c$ and $d$ respectively such that $(a - d) . (b - c) = (b - d) . (c - a) = 0$ The point $D$ , then, is the... of the $Δ A BC$ .

$(a - d) \cdot (b - c) = (b - d) \cdot (c - a) = 0$
$\Rightarrow A D ⊥ BC$ and $B D ⊥ C A$
which clearly represents from figure that $D$ is
orthocentre of $Δ A BC$