A vector v→ in the first octant is inclined to the x axis at 60°, to the y-axis at 45° and to the z-axis at an acute angle. If a plane passing through…

Question

A vector v→ in the first octant is inclined to the x axis at 60°, to the y-axis at 45° and to the z-axis at an acute angle. If a plane passing through the points √2,-1,1 and a,b,c, is normal to v→, then

MARKS Content Team · Accepted Answer

Correct answer: (C) a+√2b+c=1. Direction cosines l,m and n of given vector v→, l=cos60^(∘)=1/2 m=cos45^(∘)=(1√2n=cosγv→=cos60°i^+cos45°j^+cosγk^....(1)We know,l^2+m^2+n^2=1⇒1)/4+1/2+cos^2γ=1 (γ→Acute) ⇒cosγ=1/2 ⇒ γ=60° Equation of plane is 1/2x-√2+(1√2y+1+1)/2z-1=0 ⇒x/2+(y√2+z)/2=1/2 ⇒ x+√2y+z=1 a,b,c lies on it, ⇒ a+√2b+c=1

A vector $\vec{v}$ in the first octant is inclined to the $x$ axis at $60 °$ , to the $y$ -axis at $45 °$ and to the $z$ -axis at an acute angle. If a plane passing through the points $(\sqrt{2}, - 1, 1)$ and $(a, b, c)$ , is normal to $\vec{v}$ , then

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Relevant Questions

A vector v→ in the first octant is inclined to the x axis at 60°, to the y-axis at 45° and to the z-axis at an acute angle. If a plane passing through the points 2,-1,1 and a,b,c, is normal to v→, then

Solution

Relevant Questions

A vector $\vec{v}$ in the first octant is inclined to the $x$ axis at $60 °$ , to the $y$ -axis at $45 °$ and to the $z$ -axis at an acute angle. If a plane passing through the points $(\sqrt{2}, - 1, 1)$ and $(a, b, c)$ , is normal to $\vec{v}$ , then