A vectar vecn is inclined to x-axis at 45°, toy-axis at 60° and at an acute angle to z-axis. If vecn is a normal to a plane passing through the point (√2, -1, 1) then the equation of the plane is :

Question

A vectar vecn is inclined to x-axis at 45°, toy-axis at 60° and at an acute angle to z-axis. If vecn is a normal to a plane passing through the point (√2, -1, 1) then the equation of the plane is : (A) 4√2x +7y+z-2 (B) 2x +y+2z=2√2+1 (C) 3√2x-4y-3z = 7 (D) √2x-y-z = 2

Tardigrade Admin · Accepted Answer

Direction cosines of n are (1/2), (1/4), (1/2). Equation of the plane, (1/2)(x-√2)+(1/4)(y+1)+(1/2)(z-1) = 0 ⇒ 2(x-√2) + (y + 1) + 2(z-1) = 0 ⇒ 2x+y + 2z= 2√2-1 + 2 ⇒ 2x+y + 2z= 2√2+1

Q. A vectar $n$ is inclined to x-axis at $4 5^{\circ}$ , toy-axis at $6 0^{\circ}$ and at an acute angle to z-axis. If $n$ is a normal to a plane passing through the point $(2, - 1, 1)$ then the equation of the plane is :

$42 x + 7 y + z - 2$

$2 x + y + 2 z = 22 + 1$

$32 x - 4 y - 3 z = 7$

$2 x - y - z = 2$

Direction cosines of $n$ are $\frac{1}{2}, \frac{1}{4}, \frac{1}{2}$ .
Equation of the plane,
$\frac{1}{2} (x - 2) + \frac{1}{4} (y + 1) + \frac{1}{2} (z - 1) = 0$
$\Rightarrow 2 (x - 2) + (y + 1) + 2 (z - 1) = 0$
$\Rightarrow 2 x + y + 2 z = 22 - 1 + 2$
$\Rightarrow 2 x + y + 2 z = 22 + 1$

Q. A vectar n is inclined to x-axis at 45∘, toy-axis at 60∘ and at an acute angle to z-axis. If n is a normal to a plane passing through the point (2​,−1,1) then the equation of the plane is :

42​x+7y+z−2

2x+y+2z=22​+1

32​x−4y−3z=7

2​x−y−z=2