1
IIT-JEE 1991
Fill in the Blanks
+2
-0
Given that $$\overrightarrow a = \left( {1,1,1} \right),\,\,\overrightarrow c = \left( {0,1, - 1} \right),\,\overrightarrow a .\overrightarrow b = 3$$ and $$\overrightarrow a \times \overrightarrow b = \overrightarrow c ,$$ then $$\overrightarrow b \, =$$.........
2
IIT-JEE 1988
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+2
-0
The components of a vector $$\overrightarrow a$$ along and perpendicular to a non-zero vector $$\overrightarrow b$$ are ......and .....respectively.
3
IIT-JEE 1987
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+2
-0
If the vectors $$a\widehat i + \widehat j + \widehat k,\,\,\widehat i + b\widehat j + \widehat k$$ and $$\widehat i + \widehat j + c\widehat k$$
$$\left( {a \ne b \ne c \ne 1} \right)$$ are coplannar, then the value of $${1 \over {\left( {1 - a} \right)}} + {1 \over {\left( {1 - b} \right)}} + {1 \over {\left( {1 - c} \right)}} = ..........$$
4
IIT-JEE 1987
Fill in the Blanks
+2
-0
Let $$b = 4\widehat i + 3\widehat j$$ and $$\overrightarrow c$$ be two vectors perpendicular to each other in the $$xy$$-plane. All vectors in the same plane having projecttions $$1$$ and $$2$$ along $$\overrightarrow b$$ and $$\overrightarrow c,$$ respectively, are given by ...........
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