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The given figure shows an air plant holder which is in the shape of a tetrahedron. Let , , & are…
The given figure shows an air plant holder which is in the shape of a tetrahedron. Let $A(1, 1, 1)$, $B(2, 1, 3)$, $C(3, 2, 2)$ & $D(3, 3, 4)$ are the vertices of air plant holder.
Based on the above information answer the following questions.
(i)[2.0]
The vector of $\vec{AB}$ is:
- (a)$-\hat{i} - 2\hat{k}$
- (b)$2\hat{i} + \hat{k}$
- (c)$\hat{i} + 2\hat{k}$
- (d)$-2\hat{i} - \hat{k}$
(ii)[2.0]
The vector of $\vec{AC}$ is:
- (a)$2\hat{i} - \hat{j} - \hat{k}$
- (b)$2\hat{i} + \hat{j} + \hat{k}$
- (c)$-2\hat{i} - \hat{j} + \hat{k}$
- (d)$\hat{i} + 2\hat{j} + \hat{k}$
(iii)[2.0]
Area of $\Delta ABC$ is:
- (a)$\frac{\sqrt{11}}{2}\text{ Sq. units}$
- (b)$\frac{\sqrt{14}}{2}\text{ Sq. units}$
- (c)$\frac{\sqrt{13}}{2}\text{ Sq. units}$
- (d)$\frac{\sqrt{17}}{2}\text{ Sq. units}$
(iv)[2.0]
The unit vector along the $\vec{AB}$ is:
- (a)$\frac{-2\hat{i} - \hat{k}}{\sqrt{5}}$
- (b)$\frac{-\hat{i} - 2\hat{k}}{\sqrt{5}}$
- (c)$\frac{2\hat{i} + \hat{k}}{\sqrt{5}}$
- (d)$\frac{\hat{i} + 2\hat{k}}{\sqrt{5}}$
Answer
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From ISC 2022 Specimen Mathematics Paper 1, question 28.