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Question: If position vector of points A, B, C are respectively **i, j, k** and \(AB = CX,\) then position vec...

If position vector of points A, B, C are respectively i, j, k and AB=CX,AB = CX, then position vector of point X is

A

−i+j+k- \mathbf{i} + \mathbf{j} + \mathbf{k}

B

i−j+k\mathbf{i} - \mathbf{j} + \mathbf{k}

C

i+j−k\mathbf{i} + \mathbf{j} - \mathbf{k}

D

i+j+k\mathbf{i} + \mathbf{j} + \mathbf{k}

Answer

−i+j+k- \mathbf{i} + \mathbf{j} + \mathbf{k}

Explanation

Solution

AB→=CX→⇒j−i=P.V.ofX−k⇒P.V.ofX=−i+j+k\overset{\rightarrow}{AB} = \overset{\rightarrow}{CX} \Rightarrow \mathbf{j} - \mathbf{i} = \text{P.V.of}X - \mathbf{k} \Rightarrow \text{P.V.of}X = - \mathbf{i} + \mathbf{j} + \mathbf{k}.