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Question

Vector equation of a straight line passing through a point given by position vector ¯a parallel to ¯b be is given by ¯r=¯aλ ¯b, where ¯r , where ¯r is r position vector of a general point on the line and λϵIR


A

True

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B

False

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Solution

The correct option is A

True


Let’s consider the point ¯a and vector ¯b

The line parallel to ¯b and passing through ¯a will be something like this

You can clearly see if we shift ¯b and do ¯a+¯b we get a point on the line.

Moreover, if we keep changing the magnitude of ¯b and add it to ¯a we will still get a resultant which lies on the line.

Therefore the points of the line required will be ¯a+λ¯b where λϵIR. Here the value of λ is both +ve and –ve. So without loss of generality we can have it as ¯aλ¯b where λϵIR. Therefore the given statement is true.


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