Home
Class 12
MATHS
A and B are two points with coordinates ...

A and B are two points with coordinates `(x_(1),y_(1),z_(1))` and `(x_(2),y_(2),z_(2))`, respectively, in space. Let P and Q be feet of the perpendicular drawn from A and B to a line L whose direction ratios are l,m,n. Let `theta` be the angle between AB and L then find the value of `cos theta`

A

`PQ=Abcostheta`

B

`PQ=|(x_(2)-x_(1))l+(y_(2)-y_(1))m+(z_(2)-z_(1))n|`

C

`PQ=(|(x_(2)-x_(1))l+(y_(2)-y_(1))m+(z_(2)-z_(1))n|)/(sqrt(l^(2)+m^(2)+n^(2))`

D

AB and PQ are always coplanar.

Text Solution

Verified by Experts

The correct Answer is:
A, C
DC's of AB are `(x_(2)-x_(1))/(AB), (y_(2)-y_(1))/(AB), (z_(2)-z_(1))/(AB)`
DC's of L are
`l/sqrt(l^(2)+m^(2)+n^(2)), m/sqrt(l^(2)+m^(2)+n^(2)),n/sqrt(l^(2)+m^(2)+n^(2))`
`costheta=(((x_(2)-x_(1))l+(y_(2)-y_(1))m+(z_(2)-z_(1))n)/sqrt(l^(2)+m^(2)+n^(2)))`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|246 Videos

Similar Questions

Explore conceptually related problems

Find the distance between the points P(x_(1),y_(1),z_(1)) and Q(x_(2),y_(2),z_(2))

Planes r drawn parallel to the coordinate planes through the point P(x_(1),y_(1),z_(1) and Q(x_(2),y_(2),z_(2)). Find the length of the edges of the parallelepiped so formed.

If l_(1),m_(1),n_(1) and l_(2),m_(2),n_(2) are the directional cosines of two vectors and theta is the angle between them, then their value of cos theta is

If theta is the angle between two lines whose d.c's are (l_(1),m_(1),n_(1)) and (l_(2),m_(2),n_(2)) then the lines are perpendicular if and only if

If ' P' divides the line segment joining A(x_(1),y_(1),z_(1)),B(x_(2),y_(2),z_(2)) in the ratio m : n internally then P=

The direction cosines of the lines bisecting the angle between the line whose direction cosines are l_1, m_1, n_1 and l_2, m_2, n_2 and the angle between these lines is theta , are

Let A,B,C be the feet of perpendiculars drawn from a point P to x, y aned z-axses respectively. Find the coordinates of A,B,C if coordinates of P are: (3,1,2)