1
IIT-JEE 1994
Fill in the Blanks
+2
-0
A unit vector perpendicular to the plane determined by the points $$P\left( {1, - 1,2} \right)Q\left( {2,0, - 1} \right)$$ and $$R\left( {0,2,1} \right)$$ is ............
2
IIT-JEE 1994
MCQ (Single Correct Answer)
+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
$$4p = 9q$$
3
IIT-JEE 1994
MCQ (Single Correct Answer)
+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
4
IIT-JEE 1994
MCQ (More than One Correct Answer)
+4
-1
The vector $$\,{1 \over 3}\left( {2\widehat i - 2\widehat j + \widehat k} \right)$$ is
A
a unit vector
B
makes an angle $${\pi \over 3}$$ with the vector $$\left( {2\widehat i - 4\widehat j + 3\widehat k} \right)$$
C
parallel to the vector $$\left( { - \widehat i + \widehat j - {1 \over 2}\widehat k} \right)$$
D
perpendicular to the vector $${3\widehat i + 2\widehat j - 2\widehat k}$$
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