A) \[\mathbf{r}.(20\mathbf{i}-8\mathbf{j}+5\mathbf{k})=120\]
B) \[\mathbf{r}.(20\mathbf{i}-8\mathbf{j}+5\mathbf{k})=1\]
C) \[\mathbf{r}.(20\mathbf{i}-8\mathbf{j}+5\mathbf{k})=2\]
D) \[\mathbf{r}.(20\mathbf{i}-8\mathbf{j}+5\mathbf{k})=20\]
Correct Answer: A
Solution :
Centroid of \[\Delta PQR\] is \[2\mathbf{i}-5\mathbf{j}+8\mathbf{k}\] \[\therefore \] Intercepts on x, y and z axis are \[6\mathbf{i},\,-15\mathbf{j}\] and \[24\mathbf{k}\] respectively. Hence equation of plane is, \[[\mathbf{r}-15\mathbf{j}\,\,\,24\mathbf{k}]+[\mathbf{r}\,\,24\mathbf{k}\,\,6\mathbf{i}]+[\mathbf{r}\,\,6\mathbf{i}\,\,-15\mathbf{j}]=[6\mathbf{i}\,\,\,-15\mathbf{j}\,\,24\mathbf{k}]\] \[\therefore \] \[-\mathbf{r}.(20\mathbf{i}-8\mathbf{j}+5\mathbf{k})=-120\] \[\therefore \] \[\mathbf{r}.(20\mathbf{i}-8\mathbf{j}+5\mathbf{k})=120\].
You need to login to perform this action.
You will be redirected in
3 sec
