Practicing Success
A ball is thrown upwards from the plane surface of the ground. Suppose the plane surface from which the ball is thrown also 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 ΔABC is : |
$\sqrt{29}$ sq. units $\frac{1}{4} \sqrt{29}$ sq. units $\frac{1}{16} \sqrt{29}$ sq. units $\frac{1}{2} \sqrt{29}$ sq. units |
$\frac{1}{2} \sqrt{29}$ sq. units |
$\vec{CA} = -2\hat{j} + \hat{k}$ $\vec{CB} = 2\hat{i} - 3\hat{j}$ ar(ABC) = $\frac{1}{2} |\vec{CA} × \vec{CB}|$ $|\vec{CA} × \vec{CB}| = |\vec{n}| = |3\hat{i} + 2\hat{j} + 4\hat{k}|$ = $\sqrt{3^2+2^2+4^2}$ = $\sqrt{9+4+16} = \sqrt{29}$ so ar(ABC) = $\frac{1}{2} \sqrt{29}$ sq. units |