Question 17

Mathematics Scalar and Vector Products Medium

The equation of the plane passing through the point \((1,2,3)\) and having the vector \(\bar{N}=3 i-j+2 k\) as its normal is

(A) \(2 x-y+3 z+7=0\)
(B) \(3 x-y+2 z+7=0\)
(C) \(3 x-y+2 z=7\)
(D) \(3 x+y+2 z=7\)
✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Equation of the plane passing through \((1,2,3)\) and having the vector \(\bar{N}=3 i-j+2 k\) as its normal is \[\] \(\Rightarrow 3(x-1)+-1(y-2)+2(z-3)=0\) \[\] \(\Rightarrow 3 x-y+2 z-3+2-6=0\) \[\] \(3 x-y+2 z=7\) \[\] Choice (C)

Practice Similar Scalar and Vector Products Questions

Reinforce your conceptual grasp with related questions from NIMCET 2012:

Q7 If the vectors \( a =(1, x,-2)\) and \( b =(x, 3,-4)\) are mutually...
Solve →
Q28 If \( a + b + c =0,| a |=3,| b |=5,| c |=7\), then angle between the...
Solve →
Q29 If \(θ(0 ≤ θ ≤ π)\) is the angle between the vectors \( a \) and \( b \),...
Solve →
Q35 If \( a , b \) and \( c \) are unit vectors such that \( a + b + c =0\),...
Solve →
Q36 If \( a , b , c \) are non-coplanar vectors and \(λ\) is a real number,...
Solve →
Full-Length Test Series

Prepare for NIMCET Under Real Exam Conditions

Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.

Start Free Mock Test Series →