1
IIT-JEE 1985
Fill in the Blanks
+2
-0
If $$\overrightarrow A = \left( {1,1,1} \right),\,\,\overrightarrow C = \left( {0,1, - 1} \right)$$ are given vectors, then a vector $$B$$ satifying the equations $$\overrightarrow A \times \overrightarrow B = \overrightarrow {\,C}$$ and $$\overrightarrow A .\overrightarrow B = \overrightarrow {3\,}$$ ..........
2
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 $$ABC.$$

3
IIT-JEE 1983
Fill in the Blanks
+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 ...........
4
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 ..........
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