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

Equation of a Plane Passing through a Point and Parallel to the Two Given Vectors

The length of...

Question

The length of perpendicular from $(0, 0, 0)$ to the plane passing three non collinear points $\to a, \to b, \to c$ is

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

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

[a b c]

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

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

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

[a b c]^{2}

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

Open in App

Solution

The correct option is B $\frac{[\to a, \to b, \to c]}{\to a \times \to b \times + \to b \times \to c + \to c \times \to a}$
The given plane passes through $\to a$ , $\to b$ and $\to c$
So, it is normal to $(\to b - \to a) \times (\to c - \to b)$ .
Hence , its equation is
$(\to r - \to a \cdot ((\to b - \to a) \times (\to c - \to b))) = 0$
$\to r \cdot (\to a \times \to b + \to b \times \to c + \to c \times \to a) = [\to a \to b \to c]$
Therefore, the length of perpendicular from the origin to this plane is
$= \frac{[\to a \to b \to c]}{∣ \to a \times \to b + \to b \times \to c + \to c \times \to a ∣}$

Suggest Corrections

Similar questions

\to a, \to b, \to c

\to r

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)

\to a, \to b, \to c

\to a, \to b, \to c

\to a, \to b, \to c

\to a + \to b

\to c

\to a + \to c

\to b

\to a, \to b, \to c

3, 4, 5

\to a

\to b + \to c, \to b

\to c + \to a

\to c

\to a + \to b .

∣ ∣ \to a + \to b + \to c ∣ ∣

Join BYJU'S Learning Program