1
IIT-JEE 1995 Screening
+4
-1
Let $$\overrightarrow u ,\overrightarrow v$$ and $$\overrightarrow w$$ be vectors such that $$\overrightarrow u + \overrightarrow v + \overrightarrow w = 0.$$ If $$\left| {\overrightarrow u } \right| = 3,\left| {\overrightarrow v } \right| = 4$$ and $$\left| {\overrightarrow w } \right| = 5,$$ then $$\overrightarrow u .\overrightarrow v + \overrightarrow v .\overrightarrow w + \overrightarrow w .\overrightarrow u$$ is
A
$$47$$
B
$$-25$$
C
$$0$$
D
$$25$$
2
IIT-JEE 1995 Screening
+4
-1
If $$\overrightarrow a ,$$ $$\overrightarrow b$$ and $$\overrightarrow c$$ are three non coplanar vectors, then
$$\left( {\overrightarrow a + \overrightarrow b + \overrightarrow c } \right).\left[ {\left( {\overrightarrow a + \overrightarrow b } \right) \times \left( {\overrightarrow a + \overrightarrow c } \right)} \right]$$ equals
A
$$0$$
B
$$\left[ {\overrightarrow a \,\overrightarrow b \,\overrightarrow c } \right]$$
C
$$2\left[ {\overrightarrow a \,\overrightarrow b \,\overrightarrow c } \right]$$
D
$$-\left[ {\overrightarrow a \,\overrightarrow b \,\overrightarrow c } \right]$$
3
IIT-JEE 1994
+4
-1
Let $$\overrightarrow p$$ and $$\overrightarrow q$$ be the position vectors of $$P$$ and $$Q$$ respectively, with respect to $$O$$ and $$\left| {\overrightarrow p } \right| = p,\left| {\overrightarrow q } \right| = q.$$ The points $$R$$ and $$S$$ divide $$PQ$$ internally and externally in the ratio $$2:3$$ respectively. If $$OR$$ and $$OS$$ are perpendicular then
A
$$9{q^2} = 4{q^2}$$
B
$$4{p^2} = 9{q^2}$$
C
$$9p = 4q$$
D
$$4p = 9q$$
4
IIT-JEE 1994
+4
-1
Let $$\alpha ,\beta ,\gamma$$ be distinct real numbers. The points with position
vectors $$\alpha \widehat i + \beta \widehat j + \gamma \widehat k,\,\,\beta \widehat i + \gamma \widehat j + \alpha \widehat k,\,\,\gamma \widehat i + \alpha \widehat j + \beta \widehat k$$
A
are collinear
B
form an equilateral triangle
C
form a scalene triangle
D
form a right-angled triangle
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