Q. 20

# Find the distance of the point (–1, –5, –10), from the point of intersection of the line and the plane **[CBSE 2011]**

**[CBSE 2011]**

Answer :

Given, the equation of the line is –

The cartesian form of the equation is –

∴ x = 3λ + 2 …(1)

y = 4λ – 1 …(2)

and z = 2λ + 2 …(3)

Given equation of plane is –

The cartesian form of above equation is –

x – y + z = 5 …(4)

At the point of intersection of line and the plane-

We have –

3λ +2 – (4λ – 1) + (2λ + 2) = 5

⇒ λ + 5 = 5

∴ λ = 0

Hence, x = 2 ; y = -1 and z = 2

∴ position vector of the intersection point is or coordinate is (2,-1,2)

By distance formula, we know that distance between two points (x_{1},y_{1},z_{1}) and (x_{2},y_{2},z_{2}) is given by –

∴ distance between (-1, -5, -10) and (2,-1, 2) is given by –

⇒ D = = 13 units.

Hence, a distance of the point (–1, –5, –10), from the point of intersection of the line and the plane is 13 units

Rate this question :

If lines and intersect, then find the value of k and hence find the equation of the plane containing these lines.

Mathematics - Board PapersFind the coordinates of the point where the line through the points A(3, 4, 1) and B(5, 1, 6) crosses the XZ plane. Also find the angle which this line makes with the XZ plane.

Mathematics - Board PapersState True or False for the statements

The angle between the lineand the plane is .

Mathematics - ExemplarThe sine of the angle between the straight lineand the plane 2x – 2y + z = 5 is

Mathematics - ExemplarThe plane 2x – 3y + 6z – 11 = 0 makes an angle sin^{–1}(α) with x-axis. The valueof α is equal to

Mark against the correct answer in each of the following:

The angle between the line and the plane 2x – 3y + z = 5 is

RS Aggarwal - Mathematics

Mark against the correct answer in each of the following:

The angle between the line and the plane is

RS Aggarwal - Mathematics