If \( O A B C \) is a tetrahedron with equal edges and \( \hat{\mat...
If \( O A B C \) is a tetrahedron with equal edges and \( \hat{\mathbf{p}}, \hat{\mathbf{q}}, \hat{\mathbf{r}} \) are unit vectors along bisectors of \( \overrightarrow{\mathbf{O A}}, \overrightarrow{\mathbf{O B}}: \overrightarrow{\mathbf{O B}}, \overrightarrow{\mathbf{O C}}: \overrightarrow{\mathbf{O C}}, \overrightarrow{\mathbf{O A}} \) respectively and \( \hat{\mathbf{a}}=\frac{\overrightarrow{\mathbf{O A}}}{|\overrightarrow{\mathbf{O A}}|}, \overrightarrow{\mathbf{b}}=\frac{\overrightarrow{\mathbf{O B}}}{|\overrightarrow{\mathbf{O B}}|}, \overrightarrow{\mathbf{c}}=\frac{\overrightarrow{\mathbf{O C}}}{|\overrightarrow{\mathbf{O C}}|} \), then :
\( \mathrm{P} \)
(a) \( \frac{[\hat{\mathbf{a}} \hat{\mathbf{b}} \hat{\mathbf{c}}]}{[\hat{\mathbf{p}} \hat{\mathbf{q}} \hat{\mathbf{r}}]}=\frac{3 \sqrt{3}}{2} \)
(b) \( \frac{[\hat{\mathbf{a}}+\hat{\mathbf{b}} \hat{\mathbf{b}}+\hat{\mathbf{c}} \hat{\mathbf{c}}+\hat{\mathbf{a}}]}{[\hat{\mathbf{p}}+\hat{\mathbf{q}} \hat{\mathbf{q}}+\hat{\mathbf{r}} \hat{\mathbf{r}}+\hat{\mathbf{p}}]}=\frac{3 \sqrt{3}}{4} \)
(c) \( \frac{[\hat{\mathbf{a}}+\hat{\mathbf{b}} \hat{\mathbf{b}}+\hat{\mathbf{c}} \hat{\mathbf{c}}+\hat{\mathbf{a}}]}{[\hat{\mathbf{p}} \hat{\mathbf{q}} \hat{\mathbf{r}}]}=\frac{3 \sqrt{3}}{2} \)
(d) \( \frac{[\hat{\mathbf{a}} \hat{\mathbf{b}} \hat{\mathbf{c}}]}{[\hat{\mathbf{p}}+\hat{\mathbf{q}} \hat{\mathbf{q}}+\hat{\mathbf{r}} \hat{\mathbf{r}}+\hat{\mathbf{p}}]}=\frac{3 \sqrt{3}}{4} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-03-21 | Let \( a, b \) are positive real numbers such that \( a-b=10 \), th... |
| 2023-03-21 | Let \( f(x)=-x^{100} \). If \( f(x) \) is divided by \( x^{2}+x \),... |
| 2023-03-21 | Let \( f: D \rightarrow R \) be defined as \( f(x)=\frac{x^{2}+2 x+... |
| 2023-03-21 | If \( f(x)=\pi\left(\frac{\sqrt{x+7}-4}{x-9}\right) \), then the ra... |
| 2023-03-21 | If the equation \( \left(p^{2}-4\right)\left(p^{2}-9\right) x^{3}+\... |
| 2023-03-21 | Let \( |\overrightarrow{\mathbf{a}}|=1,|\overrightarrow{\mathbf{b}}... |
| 2023-03-21 | The vertices of \( \triangle A B C \) are \( A(2,0,0), B(0,1,0), C(... |
| 2023-03-21 | \( A B C D \) is a regular tetrahedron, \( A \) is the origin and \... |
| 2023-03-21 | In above problem find the largest possible value of \( |\overrighta... |
| 2023-03-21 | The vertices of \( \triangle A B C \) are \( A(2,0,0), B(0,1,0), C(... |
| 2023-03-21 | If \( O A B C \) is a tetrahedron with equal edges and \( \hat{\mat... |
| 2023-03-21 | Range of \( f(x)=\sin ^{-1}[x-1]+2 \cos ^{-1}[x-2] \) ([.] denotes ... |
| 2023-03-21 | \( \Lambda \) solution of the equation \( \cot ^{-1} 2=\cot ^{-1} x... |
| 2023-03-21 | Number of perpendicular tangents that can be drawn on the ellipse \... |
| 2023-03-21 | The number of ways in which \( 2 n \) objects of one type, \( 2 n \... |
| 2023-03-21 | Four couples (husband and wife) decide to form a committee of four ... |
| 2023-03-21 | Let \( N \) be the number of integral solution of the equation \( x... |
| 2023-03-21 | There are \( n \) persons sitting around a circular table. They sta... |
| 2023-03-21 | The number of ways to choose 7 distinct natural numbers from the fi... |
| 2023-03-21 | 8 clay targets are arranged as shown. If \( N \) be the number of d... |
| 2023-03-21 | The number of triangles with each side having integral length and t... |
0