Find the projection of the line segment joining the points (2, -3, 0), (0, 4, 5) on the line with direction cosines $2 over 3 comma space 3 over 7 comma space minus 6 over 7$

Solution

P, Q are the points (2, –3, 0), (0, 4, 5) and direction cosines of line AB are $2 over 7 comma space 3 over 7 comma space minus 6 over 7$
$therefore$ projection of PQ on AB = $open vertical bar left parenthesis 0 minus 2 right parenthesis space open parentheses 2 over 3 close parentheses plus left parenthesis 4 minus 3 right parenthesis space open parentheses 3 over 7 close parentheses plus left parenthesis 5 minus 0 right parenthesis space open parentheses negative 6 over 7 close parentheses close vertical bar$
$equals space open vertical bar negative 4 over 7 plus 21 over 7 minus 30 over 7 close vertical bar space equals space open vertical bar negative 4 over 7 minus 9 over 7 close vertical bar equals space open vertical bar fraction numerator negative 4 minus 9 over denominator 7 end fraction close vertical bar space equals space 13 over 7$

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Three Dimensional Geometry

Find the projection of the line segment joining the points (2, -3, 0), (0, 4, 5) on the line with direction cosines $2 over 3 comma space 3 over 7 comma space minus 6 over 7$

Some More Questions From Three Dimensional Geometry Chapter

Find the direction cosines of x, y and z-axis.

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