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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 area of $\triangle ABC$ is:
Solution
$A(1,0,2)$ $B(3,-1,1)$ $C(1,2,1)$ Vectors $\vec{AB}=(3-1,-1-0,1-2)=(2,-1,-1)$ $\vec{AC}=(1-1,2-0,1-2)=(0,2,-1)$ Cross product $\vec{AB}\times\vec{AC}$ $= \begin{vmatrix} \mathbf{i}&\mathbf{j}&\mathbf{k}\\ 2&-1&-1\\ 0&2&-1 \end{vmatrix} $ $=3\mathbf{i}+2\mathbf{j}+4\mathbf{k}$ Magnitude $|\vec{AB}\times\vec{AC}|$ $=\sqrt{3^2+2^2+4^2}$ $=\sqrt{29}$ Area of triangle $=\frac{1}{2}|\vec{AB}\times\vec{AC}|$ $=\frac{1}{2}\sqrt{29}$Online Test Series, Information About Examination,
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