The coordinates of a point on the line x-4 y-5- z-3 y-6 at a distance 3 -26 from the point 5-0-6 areA- 17-3-3B- -7-3-15C- -17-3-3D- 7-3-15

The correct option is A (17, 3, 3)Line is x 5/4/√(26) = y/1/√(26) = z+6/3/√(26) A point on this line at a distance 3 √(26) from (5, 0, 6) is (5 ± (3 × 4), ± 3 ...

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Standard XII

Mathematics

Section Formula

The coordinat...

Question

The coordinates of a point on the line x = 4y + 5, z = 3y - 6 at a distance $3 \sqrt{26}$ from the point (5, 0, -6)are

(17, 3, 3)

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(-7, 3, -15)

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(-17, -3, -3)

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(7, -3, 15)

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Solution

The correct option is A (17, 3, 3)
Line is $\frac{x - 5}{\frac{4}{\sqrt{26}}} = \frac{y}{\frac{1}{\sqrt{26}}} = \frac{z + 6}{\frac{3}{\sqrt{26}}}$ A point on this line at a distance $3 \sqrt{26}$ from (5, 0, -6) is
$(5 \pm (3 \times 4), \pm 3, - 6 \pm 9) = (17, 3, 3) o r (- 7, - 3, - 15) .$

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Similar questions

Q. Which of the following is "CORRECT" option?

\begin{matrix} List I & List II (a) The coordinates of a point on the line x = 4 y + 5, z = 3 y - 6 at a distance 3 from the point (5, 3, - 6) is/are & (p) (- 1, - 2, 0) (b) The plane containing the lines \frac{x - 2}{3} = \frac{y + 3}{5} = \frac{z + 5}{7} and parallel to^i + 4^j + 7^k has (q) (5, 0, - 6) (c) A line passes through two points A (2, - 3 -, 1) and B (8, - 1, 2) . The coordinates of a point on this line farthest to the origin and at a distance of 14 units from A is & (r) (2, 5, 7) (d) The coordinates of the foot of the perpendicular from the point (3, - 1, 11) on the line \frac{x}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} is/are & (s) (14, 1, 5) \end{matrix}

Q. The point(s) on the

x -

axis which is (are) at a distance of

5

units from the point

(6, - 3),

is (are)

Q. Find the coordinates of those points on the line

\frac{x + 1}{2} = \frac{y + 2}{3} = \frac{z - 3}{6}

which is at a distance of

3

units from the point

(1, - 2, 3)

Q. Which of the following is "CORRECT" option?

\begin{matrix} List I & List II (a) The coordinates of a point on the line x = 4 y + 5, z = 3 y - 6 at a distance 3 from the point (5, 3, - 6) is/are & (p) (- 1, - 2, 0) (b) The plane containing the lines \frac{x - 2}{3} = \frac{y + 3}{5} = \frac{z + 5}{7} and parallel to^i + 4^j + 7^k has (q) (5, 0, - 6) (c) A line passes through two points A (2, - 3 -, 1) and B (8, - 1, 2) . The coordinates of a point on this line farthest to the origin and at a distance of 14 units from A is & (r) (2, 5, 7) (d) The coordinates of the foot of the perpendicular from the point (3, - 1, 11) on the line \frac{x}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} is/are & (s) (14, 1, 5) \end{matrix}

Q. Coordinates of a point which is at

3

units distance from the point

(1, - 3)

on the line

2 x + 3 y + 7 = 0

is/are

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The coordinates of a point on the line x = 4y + 5, z = 3y - 6 at a distance 3√26 from the point (5, 0, -6)are

The correct option is A (17, 3, 3)Line is x−54√26=y1√26=z+63√26 A point on this line at a distance 3√26 from (5, 0, -6) is (5±(3×4),±3,−6±9)=(17,3,3)or(−7,−3,−15).

The coordinates of a point on the line x = 4y + 5, z = 3y - 6 at a distance $3 \sqrt{26}$ from the point (5, 0, -6)are

The correct option is A (17, 3, 3)
Line is $\frac{x - 5}{\frac{4}{\sqrt{26}}} = \frac{y}{\frac{1}{\sqrt{26}}} = \frac{z + 6}{\frac{3}{\sqrt{26}}}$ A point on this line at a distance $3 \sqrt{26}$ from (5, 0, -6) is
$(5 \pm (3 \times 4), \pm 3, - 6 \pm 9) = (17, 3, 3) o r (- 7, - 3, - 15) .$