Ts Eamcet
Vector Algebra
TS EAMCET 2020 (Online) 11th September Morning Shift
MCQ+1 / -02020
If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are the position vectors of the points $A, B, C$ respectively, then match the items of list-I with those of list-II.
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| \( \text { List-I } \) | \( \text { List-II } \) | ||
|---|---|---|---|
| A. | $$ \text { } \begin{aligned} \mathbf{a} & =2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \\ \mathbf{b} & =3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, \\ \mathbf{c} & =4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}} \end{aligned} $$ | I. | $A, B, C$ are collinear |
| B. | $$ \text { } \begin{aligned} \mathbf{a} & =\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \\ \mathbf{b} & =3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}, \\ \mathbf{c} & =-3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-5 \hat{\mathbf{k}} \end{aligned} $$ | II. | $\triangle A B C$ is an isosceles triangle |
| C. | $$ \begin{aligned} &\text { }\\ &\begin{aligned} & a=2 \hat{i}-\hat{j}+\hat{k}, \\ & b=\hat{i}-3 \hat{j}-5 \hat{k}, \\ & c=-3 \hat{i}-4 \hat{j}-4 \hat{k} \end{aligned} \end{aligned} $$ | III. | $\triangle A B C$ is a right-angled triangle |
| D. | $$ \begin{aligned} & a=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \\ & b=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \\ & c=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \end{aligned} $$ | IV. | $\triangle A B C$ is a right-angled isosceles triangle |
| V. | \( \triangle A B C \text { is an equilateral triangle } \) | ||
\(\text { The correct match is }\)