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The equation of the passing through $(1, 0, 3)$ and having direction cosines $a, b, \frac{1}{2}$ in
Symmetric form is $\frac{x - 1}{a} = \frac{y}{b} = \frac{z - 3}{\frac{1}{2}}$ then $a^{2} + b^{2}$ is

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a

34

b

12

c

14

d

0

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Correct option is A

The Equation of the line passing through the point (x1,y1,z1) and having direction ratios ⟨a,b,c⟩ is x−x1a=y−y1b=z−z1cThe equation of the line passing through the point (1,0,3) and having direction cosines a,b,12 is x−1a=y−0b=z−312since a,b,12 are direction cosines of the line, then a2+b2+14=1⇒a2+b2=34

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