TS EAMCET · Maths · Vector Algebra
If \(\mathrm{A}(1,2,3), \mathrm{B}(3,7,-2), \mathrm{C}(6,7,7)\) and \(\mathrm{D}(-1,0,-1)\) are points in a plane, then the vector equation of the line passing through the centroids of \(\triangle \mathrm{ABD}\) and \(\triangle \mathrm{ACD}\) is
- A \(\overrightarrow{\mathrm{r}}=(2 \hat{\mathrm{i}}-\hat{\mathrm{j}})+\mathrm{t}(\hat{\mathrm{j}}+4 \hat{\mathrm{k}})\)
- B \(\overrightarrow{\mathrm{r}}=(1+t) \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+3 \mathrm{t} \hat{\mathrm{k}}\)
- C \(\overrightarrow{\mathrm{r}}=(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})+\mathrm{t}(\hat{\mathrm{i}}+3 \hat{\mathrm{j}})\)
- D \(\vec{r}=(\hat{i}+\hat{j}+\hat{k})+t(2 \hat{i}-\hat{j})\)
Answer & Solution
Correct Answer
(B) \(\overrightarrow{\mathrm{r}}=(1+t) \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+3 \mathrm{t} \hat{\mathrm{k}}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{A}(1,2,3) ; \mathrm{B}(3,7,-2) ; \mathrm{C}(6,7,7) ; \mathrm{D}(-1,0,-1)\) Centroid of \(\triangle \mathrm{ABD}=(1,3,0)\) Centroid of \(\triangle \mathrm{ACD}=(2,3,3)\) Equation of vector passing through \(\vec{a}\) and \(\vec{b}\)…
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