1
IIT-JEE 1984
Fill in the Blanks
+2
-0
$$A, B, C$$ and $$D,$$ are four points in a plane with position vectors $$a, b, c$$ and $$d$$ respectively such that $$\left( {\overrightarrow a - \overrightarrow d } \right)\left( {\overrightarrow b - \overrightarrow c } \right) = \left( {\overrightarrow b - \overrightarrow d } \right)\left( {\overrightarrow c - \overrightarrow a } \right) = 0$$\$

The point $$D,$$ then, is the ................ of the triangle $$ABC.$$

2
IIT-JEE 1983
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+1
-0
The unit vector perpendicular to the plane determined by $$P\left( {1, - 1,2} \right),\,Q\left( {2,0, - 1} \right)$$ and $$R\left( {0,2,1} \right)$$ is ...........
3
IIT-JEE 1983
Fill in the Blanks
+1
-0
The area of the triangle whose vertices are $$A(1, -1, 2), B(2, 1, -1), C(3, -1, 2)$$ is ..........
4
IIT-JEE 1981
Fill in the Blanks
+2
-0
Let $$\overrightarrow A ,\overrightarrow B ,\overrightarrow C$$ be vectors of length $$3, 4, 5$$ respectively. Let $$\overrightarrow A$$ be perpendicular to $$\overrightarrow B + \overrightarrow C ,\overrightarrow B$$ to $$\overrightarrow C + \overrightarrow A$$ to $$\overrightarrow A + \overrightarrow B .$$ Then the length of vector $$\overrightarrow A + \overrightarrow B + \overrightarrow C$$ is ..........
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