Home
Class 12
MATHS
If A(-4,0,3)a n dB(14 ,2,-5), then which...

If `A(-4,0,3)a n dB(14 ,2,-5),` then which one of the following points lie on the bisector of the angle between ` vec O Aa n d vec O B(O` is the origin of reference )? a. `(2,2,4)` b. `(2, 11 ,5)` c. `(-3,-3,-6)` d. `(1,1,2)`

A

(2,2,4)

B

(2,11,5)

C

(-3,-3,-6)

D

(1,1,2)

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`OA=-4hati+3hatk,OB=14hati+2hatj-5hatk`
`a=(-4hati+3hatk)/(5),b=(14hati+2hatj-5hatk)/(15)`
`r=(lamda)/(15)[12hati+9hatj+14 hati+2hatj-5hatk]`
`=(lamda)/(15)[2hati+2hatj+4hatk]=(2lamda)/(15)[hati+hatj+2hatk]`.
Promotional Banner

Similar Questions

Explore conceptually related problems

State in which quadrant does each of the following points lie : (-2, 4), (3, -1), (1, 2), (-3, -5)

Find the position vectors of the points which divide the join of the points 2 vec a-3 vec ba n d3 vec a-2 vec b internally and externally in the ratio 2:3 .

|vec(a)|=3,|vec(b)=(sqrt(2))/(3) . If vec(a)xx vec(b) is a unit vector then find the angle between vec(a) and vec(b) .

Find the angel between the planes 2x+y-2z+3=0a n d vec rdot(6 hat i+3 hat j+2 hat k)=5.

The vector vec c , directed along the internal bisector of the angle between the vectors vec a = 7 hati - 4 hatj - 4hatk and vecb = -2hati - hatj + 2 hatk " with " |vec c| = 5 sqrt(6), is

A (1, -1, -3), B(2, 1, -2) and C(-5, 2, -6) are the verticies of DeltaABC . Find co-ordinates of point D, if bisector of angleA intersects bar(BC) at point D.

If vec a , vec b are the position vectors of the points (1,-1),(-2,m), find the value of m for which vec aa n d vec b are collinear.

If A(3,2,-4),B(4,3,-4),C(3,3,3) and D(4, 2,-3) are given then find the projection of vec(AD) on vec(AB)xx vec(AC) .

Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixed points on the parabola. Let C be a moving point on the parabola between Aa n dB such that the area of the triangle A B C is maximum. Then the coordinates of C are (1/4,1) (b) (4,4) (3,2/(sqrt(3))) (d) (3,-2sqrt(3))

A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3} , then find the following sets. A - B