A line with positive direction cosines passes through the point $$A1$$,$$2$$,−$$1and$$ makes equal angles with the coordinate axes. The line meets the plane $$x+2y+z=5at$$ the point B. Then the point Band length of the line segment AB¯respectively, are equal to

Question

A line with positive direction cosines passes through the point  $$A1$$,$$2$$,−$$1and$$ makes equal angles with the coordinate axes. The line meets the plane  $$x+2y+z=5at$$ the point B. Then the point Band length of the line segment AB¯respectively, are equal to

Infinity Learn · Accepted Answer

Equation of line passing through the point  $$A1$$,$$2$$,−$$1and$$ making equal angles with axes, having positive direction ratios is x−$$1=y$$−$$2=z+1General$$ point on the line is $$k+1$$,$$k+2$$,k−$$1Suppose$$ that this point lies on the plane  $$x+2y+z=5It$$ gives             $$k+1+2k+4+k$$−$$1=54k=1k=14Hence$$, the point of intersection of line and plane is $$B54$$,$$94$$,−$$34The$$ distance between  $$A1$$,$$2$$,−$$1$$,$$B54$$,$$94$$,−$$34is$$  $$AB=116+116+116=34$$

A line with positive direction cosines passes through the point $A (1, 2, - 1)$ and makes equal angles with the coordinate axes. The line meets the plane $x + 2 y + z = 5$ at the point $B$ . Then the point $B$ and length of the line segment $\bar{A B}$ respectively, are equal to

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A line with positive direction cosines passes through the point A1,2,−1and makes equal angles with the coordinate axes. The line meets the plane x+2y+z=5at the point B. Then the point Band length of the line segment AB¯respectively, are equal to

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A line with positive direction cosines passes through the point $A (1, 2, - 1)$ and makes equal angles with the coordinate axes. The line meets the plane $x + 2 y + z = 5$ at the point $B$ . Then the point $B$ and length of the line segment $\bar{A B}$ respectively, are equal to