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Any first degree equation in x, y and z ...

Any first degree equation in x, y and z represents a plane i.e., `ax+by+cz+d=0` is the general equation of a plane. If p be the length of perpendicular from the origin to a plane and d.c. of this normal is `lt l, m n gt`, then the equation of the plane in the normal form is `lx+my+nz=p_(1)`.
Vector equation of a plane passing through a point having position vector `vec(a)` and normal to vector `vec(n)` is
`(vec(r)-vec(a))vec(n)=0" or "vec(r).vec(n)=vec(a).vec(n)`
Suppose a vector `vec(n)` of magnitude `2sqrt(3)` such that it makes equal acual angles with the co-ordinate axes. If `vec(n)` is a normal to the plane containing the point `(1,-1,2)`.
The vector `vec(n)` is equal to

A

`vec( r )(hati+hatj+hatk)=2`

B

`vec( r ).(hati-hatj+hatk)=1`

C

`vec( r ).(3hati+hatj+hatk)=7`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
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