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  • How to solve this problem- The length of the projection of the line segment joining the points (5, −1, 4) and (4, −1, 3) on the plane, x+y+z=7 is :

The length of the projection of the line segment joining the points (5, −1, 4) and (4, −1, 3) on the plane, x+y+z=7 is :

  • Option 1)

    \sqrt{\frac{2}{3}}

  • Option 2)

    \frac{2}{\sqrt3}

  • Option 3)

    \frac{2}{3}

  • Option 4)

    \frac{1}{3}

 

Answers (1)

best_answer

 

Here PQ is the projection 

Also PQ = BC

AC = \widehat{AB}\cdot \widehat{BC} = (\hat{i}+ \hat{k}) \cdot \left ( \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt3} \right )

= 2/\sqrt3

Also AB = \sqrt2

AB^{}= AC^{2}+BC^{2}= 2= 4/3 + BC^{2}

BC^{2}= 2/3

BC^}= \sqrt(2/3)


Option 1)

\sqrt{\frac{2}{3}}

Option 2)

\frac{2}{\sqrt3}

Option 3)

\frac{2}{3}

Option 4)

\frac{1}{3}

Posted by

Himanshu

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