MCQ Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 12

The points (-2,14),(-6,8),(0,4),(4,10) taken in order, form

Vertices of a parallelogram taken in order are

$A(2 , -1,4)$ ;

$B(1, 0, -1)$ ,

$C(1,2,3)$ and D.

The points of trisection of the line segment joining (2, -3, 5), (3 , 1, -2) are

If the distance between the points (5,-1,7) and (c,5,1) is 9 then c=

If R divides the line segment joining p(2,3,4) and Q(4,5,6) in the ratio -3 : 2 , then the value of the parameter which represents R is

Explanation

${\textbf{Step1: Find coordinates of the point which divide two points internally.}}$

${\text{Given points are P(2,3,4) & Q(4,5,6)}}$

${\text{ratio is}}$

$= - \dfrac{3}{2} = \dfrac{m}{n}$

$\text{We know that, the coordinates of the point}$

$P(x, y, z)$

$\text{dividing the line segment}$

$\text{joining the points}$

$A(x_1, y_1, z_1)$

$\text{and}$

$B(x_2, y_2, z_2)$

$\text{in the ratio m : n internally is}$

$\text{} = \left( {\dfrac{{m{x_2} + nx_1}}{{m + n}},\dfrac{{m{y_2} + ny_1}}{{m + n}},\dfrac{{m{z_2} + nz_1}}{{m + n}}} \right)$

${\text{Let, }}$

${\text{R be}}$

$\left( {{x_{3,}}{y_{3,}}{z_3}} \right)$

$\text{R} = \left( {\dfrac{{m{x_2} + nx_1}}{{m + n}},\dfrac{{m{y_2} + ny_1}}{{m + n}},\dfrac{{m{z_2} + nz_1}}{{m + n}}} \right)$

$= \left( {\dfrac{{ - 3(4) + 2(2)}}{{ - 3 + 2}},\dfrac{{ - 3(5) + 2(3)}}{{ - 3 + 2}},\dfrac{{ - 3(6) + 2(4)}}{{ - 3 + 2}}} \right)$

$= \left( {\dfrac{-8}{{ - 1}},\dfrac{-9}{{ - 1}}, \dfrac{{-10}}{{ - 1}},} \right)$

$= (8,9,10)$

${\textbf{Thus, the value of parameter which represent R is (8,9,10). }}$

Which of the statement is true ? The coordinate planes divide the line joining the points

$\left ( 4,7,-2 \right )$ and

$\left ( -5,8,3 \right )$

CBSE Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 12 - MCQExams.com