Question

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\prime}$, 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

• A. $\sqrt{2} a-b+c=1$
• B. $a+\sqrt{2} b+c=1$
• C. $\sqrt{2} a+b+c=1$
• D. $a+b+\sqrt{2} c=1$

Answer 1

Answer: (B)

$a+\sqrt{2} b+c=1$

Answer 2

v^=cos60∘i^+cos45∘j^​+cosγk^
⇒41​+21​+cos2γ=1(γ→ Acute )
⇒cosγ=21​
⇒γ=60∘
Equation of plane is
21​(x−2​)+2​1​(y+1)+21​(z−1)=0
⇒x+2​y+z=1
(a, b, c) lies on it.
⇒a+2​b+c=1