Let a , b and c be distinct non-negative numbers. If the vectors a i ^ + a j ^ + c k ^ , i ^ + k ^ and c i ^ + c j ^ + b k ^ lie in a plane, then c is

Vector a i ^ + a j ^ + c k ^ , i ^ + k ^ and c i ^ + c j ^ + b k ^ are coplanar a 1 c a 0 c c 1 b = 0 ⇒ c 2 = ab ∴ a , b , c are in G.P.

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Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryCoordinates of a point in space, Direction cosines,Easy2 minPYQ_2005

MathematicsEasysingle choice

Let $a, b$ and $c$ be distinct non-negative numbers. If the vectors $a \hat{i} + a \hat{j} + c \hat{k}, \hat{i} + \hat{k}$ and $c \hat{i} + c \hat{j} + b \hat{k}$ lie in a plane, then $c$ is

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Solution:

Vector $a \hat{i} + a \hat{j} + c \hat{k}, \hat{i} + \hat{k}$ and $c \hat{i} + c \hat{j} + b \hat{k}$ are coplanar $a 1 c a 0 c c 1 b = 0 \Rightarrow c^{2} = ab ∴ a, b, c are in G.P.$

Stream:JEESubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Coordinates of a point in space, Direction cosines,

⏱ 2mℹ️ Source: PYQ_2005

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