Let {\bo {a}}^{\to}, {\bo {b}}^{\to}, {\bo {c}}^{\to} be the position vectors of the vertices A, B, C respectively of \triangle A B C. The vector area of \triangle A B C is :

Correct Answer is : 12{→a×→b+→b×→c+→c×→a}

\frac{1}{2}\{{\bo {a}}^{\to} \times({\bo {b}}^{\to} \times {\bo {c}}^{\to})+{\bo {b}}^{\to} \times({\bo {c}}^{\to} \times {\bo {a}}^{\to})+{\bo {c}}^{\to} \times({\bo {a}}^{\to} \times {\bo {b}}^{\to})\}

\frac{1}{2}\{{\bo {a}}^{\to} \times {\bo {b}}^{\to}+{\bo {b}}^{\to} \times {\bo {c}}^{\to}+{\bo {c}}^{\to} \times {\bo {a}}^{\to}\}

\frac{1}{2}\{{\bo {a}}^{\to}+{\bo {b}}^{\to}+{\bo {c}}^{\to}\}

\frac{1}{2}\{({\bo {b}}^{\to} \cdot {\bo {c}}^{\to}) {\bo {a}}^{\to}+({\bo {c}}^{\to} \cdot {\bo {a}}^{\to}) {\bo {b}}^{\to}+({\bo {a}}^{\to} \cdot {\bo {b}}^{\to}) {\bo {c}}^{\to}\}

EAMCET Engineering 2003 Solved Paper

Section: Mathematics

Question : 89 of 160

Marks: +1, -0

Let

→

be the position vectors of the vertices A,B,C respectively of △ABC. The vector area of △ABC is :

‌
1
2
{
→
a
×(
→
b
×
→
c
)+
→
b
×(
→
c
×
→
a
)+
→
c
×(
→
a
×
→
b
)}
‌
1
2
{
→
a
×
→
b
+
→
b
×
→
c
+
→
c
×
→
a
}
‌
1
2
{
→
a
+
→
b
+
→
c
}
‌
1
2
{(
→
b
⋅
→
c
)
→
a
+(
→
c
⋅
→
a
)
→
b
+(
→
a
⋅
→
b
)
→
c
}

Validate

Go to Question:

Prev Question

Next Question