jee-main 2023 Q87

jee-main · India · session1_30jan_shift2 Vectors 3D & Lines Normal Vector and Plane Equation

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\circ}$, to the $y$-axis at $45^{\circ}$ 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
(1) $\sqrt{2}a + b + c = 1$
(2) $a + b + \sqrt{2}c = 1$
(3) $a + \sqrt{2}b + c = 1$
(4) $\sqrt{2}a - b + c = 1$

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\circ}$, to the $y$-axis at $45^{\circ}$ 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\\
(1) $\sqrt{2}a + b + c = 1$\\
(2) $a + b + \sqrt{2}c = 1$\\
(3) $a + \sqrt{2}b + c = 1$\\
(4) $\sqrt{2}a - b + c = 1$

Paper Questions

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