The length of the perpendicular from the origin to the plane passing through three non-collinear points $\to a, \to b, \to c$ is

\frac{∣ ∣ ∣ [\to a, \to b, \to c] ∣ ∣ ∣}{∣ ∣ ∣ \to a \times \to b + \to b \times \to c + \to c \times \to a ∣ ∣ ∣}

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

\frac{2 ∣ ∣ ∣ [\to a, \to b, \to c] ∣ ∣ ∣}{∣ ∣ ∣ \to a \times \to b + \to b \times \to c + \to c \times \to a ∣ ∣ ∣}

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

∣ ∣ ∣ [\to a, \to b, \to c] ∣ ∣ ∣

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

\frac{∣ ∣ ∣ [\to a, \to b, \to c] ∣ ∣ ∣}{2 ∣ ∣ ∣ \to a \times \to b + \to b \times \to c + \to c \times \to a ∣ ∣ ∣}

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

Open in App

Solution

The correct option is A $\frac{∣ ∣ ∣ [\to a, \to b, \to c] ∣ ∣ ∣}{∣ ∣ ∣ \to a \times \to b + \to b \times \to c + \to c \times \to a ∣ ∣ ∣}$
The vector equation of the plane passing through points $\to a, \to b, \to c$ is
$r . (\to a \times \to b + \to b \times \to c + \to c \times \to a) = [\to a, \to b, \to c]$
Therefore, the length of the perpendicular from the origin to this plane is given by
$\frac{∣ ∣ ∣ [\to a, \to b, \to c] ∣ ∣ ∣}{∣ ∣ ∣ \to a \times \to b + \to b \times \to c + \to c \times \to a ∣ ∣ ∣}$

Suggest Corrections