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Write the Cartesian and Vector Equations of Y-axis.

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Question

Write the cartesian and vector equations of Y-axis.

 
Short/Brief Note
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Solution

Since y-axis passes through the the point (0, 0, 0) having position vector \[\overrightarrow{a} = 0 \hat{i} + 0 \hat{j}  + 0 \hat{k} \] and is parallel to the vector  \[\overrightarrow{b} = 0 \hat{i}  + 1 \hat{j} + 0 \hat{k} \] having direction ratios proportional to 0, 1, 0, the cartesian equation of y-axis is   

\[\frac{x - 0}{0} = \frac{y - 0}{1} = \frac{z - 0}{0}\]

\[ = \frac{x}{0} = \frac{y}{1} = \frac{z}{0}\] 

Also, its vector equation is , 

\[\overrightarrow{r} = \overrightarrow{a} + \lambda \overrightarrow{b} \]

\[ = 0 \hat{i}  + 0 \hat{j}  + 0 \hat{k}  + \lambda\left( 0 \hat{i} + \hat{j} + 0 \hat{k} \right)\]

\[ = \lambda \hat{j}  \]

 

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Chapter 27: Straight Line in Space - Very Short Answers [Page 41]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 27 Straight Line in Space
Very Short Answers | Q 2 | Page 41

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