Aspire's Library
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A ball is thrown upwards from the plane surface of the ground.
Suppose the plane surface from which the ball is thrown consists of the points
$A(1,0,2),\; B(3,-1,1)$ and $C(1,2,1)$ on it.
The highest point of the ball takes is $D(2,3,1)$ as shown in the figure.
Using this information answer the question.
The coordinates of the foot of the perpendicular drawn from the maximum height of the ball to the ground are:
Solution
Plane through points $A,B,C$ $3x+2y+4z=11$ Normal vector of plane $\vec{n}=(3,2,4)$ Point $D(2,3,1)$ Foot of perpendicular formula $\left(x_1-\frac{a(ax_1+by_1+cz_1+d)}{a^2+b^2+c^2},\; y_1-\frac{b(ax_1+by_1+cz_1+d)}{a^2+b^2+c^2},\; z_1-\frac{c(ax_1+by_1+cz_1+d)}{a^2+b^2+c^2}\right)$ Plane $3x+2y+4z-11=0$ Substitute point $D$ $3(2)+2(3)+4(1)-11$ $=6+6+4-11$ $=5$ Denominator $3^2+2^2+4^2$ $=9+4+16$ $=29$ Coordinates of foot $x=2-\frac{3(5)}{29}=\frac{43}{29}$ $y=3-\frac{2(5)}{29}=\frac{77}{29}$ $z=1-\frac{4(5)}{29}=\frac{9}{29}$ Foot of perpendicular $\left(\frac{43}{29},\frac{77}{29},\frac{9}{29}\right)$Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
