If the points A(-1,0,7), B(3,2, t), C(5, k,-2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given that the points $A(-1,0,7), B(3,2, t)$ and $C(5, k,-2)$ are collinear, the direction ratios of $AB$ and $BC$ must be proportional.$\frac{3-(

Vedclass · Accepted Answer

$-1: 2$

Vedclass · Answer

(B) Given that the points $A(-1,0,7), B(3,2, t)$ and $C(5, k,-2)$ are collinear, the direction ratios of $AB$ and $BC$ must be proportional.$\frac{3-(-1)}{5-3} = \frac{2-0}{k-2} = \frac{t-7}{-2-t}$$\frac{4}{2} = \frac{2}{k-2} = \frac{t-7}{-2-t}$$2 = \frac{2}{k-2} \Rightarrow k-2 = 1 \Rightarrow k = 3$$2 = \frac{t-7}{-2-t} \Rightarrow -4-2t = t-7 \Rightarrow 3t = 3 \Rightarrow t = 1$Thus, the points are $B(3,2,1)$ and $C(5,3,-2)$.The point $P$ is given by $P(t, k-2t, t+k) = P(1, 3-2(1), 1+3) = P(1, 1, 4)$.Let $P$ divide the line segment $BC$ in the ratio $\lambda : 1$.Using the section formula for the $x$-coordinate:$1 = \frac{\lambda(5) + 1(3)}{\lambda + 1}$$\lambda + 1 = 5\lambda + 3$$-2 = 4\lambda$$\lambda = -\frac{1}{2}$Therefore, the required ratio is $-1: 2$.

If the points $A(-1,0,7), B(3,2, t), C(5, k,-2)$ are collinear, then the ratio in which the point $P(t, k-2t, t+k)$ divides the line segment $BC$ is

Similar Questions

Find the coordinates of the point which divides the line segment joining the points $(1, -2, 3)$ and $(3, 4, -5)$ in the ratio $2:3$ externally.

The ratio in which the $yz$-plane divides the line segment joining $(-3, 4, -2)$ and $(2, 1, 3)$ is

If $A(2,-1,1)$,$B(2,5,1)$,and $C(0,-2,3)$ are the vertices of a triangle,and $D$ is the point of intersection of the side $BC$ and the internal angular bisector of angle $A$,then $AD=$

The coordinates of the point which divides the line segment joining the points $(2, -1, 3)$ and $(4, 3, 1)$ in the ratio $3 : 4$ internally are given by:

If $A(4, 7, 8)$,$B(2, 3, 4)$,and $C(2, 5, 7)$ are the vertices of a triangle $ABC$,find the length of the angle bisector of $\angle A$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module