1
IIT-JEE 1999
MCQ (More than One Correct Answer)
+3
-0.75
Let $$a$$ and $$b$$ two non-collinear unit vectors. If $$u = a - \left( {a\,.\,b} \right)\,b$$ and $$v = a \times b,$$ then $$\left| v \right|$$ is
A
$$\left| u \right|$$
B
$$\,\left| u \right| + \left| {u\,.\,a} \right|$$
C
$$\,\left| u \right| + \left| {u\,.\,b} \right|$$
D
$$\left| u \right| + u.\left( {a + b} \right)$$
2
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
Which of the following expressions are meaningful?
A
$$u\left( {v \times w} \right)$$
B
$$\left( {u \bullet v} \right) \bullet w$$
C
$$\left( {u \bullet v} \right)w$$
D
$$\,u\, \times \left( {v \bullet w} \right)$$
3
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 $${3\widehat i + 2\widehat j - 2\widehat k}$$
4
IIT-JEE 1993
MCQ (More than One Correct Answer)
+2
-0.5
Let $$\vec a = 2\hat i - \hat j + \hat k,\vec b = \hat i + 2\hat j - \hat k$$ and $$\overrightarrow c = \widehat i + \widehat j - 2\widehat k - 2\widehat k$$ be three vectors. A vector in the plane of $${\overrightarrow b }$$ and $${\overrightarrow c }$$, whose projection on $${\overrightarrow a }$$ is of magnitude $$\sqrt {2/3,}$$ is :
A
$$2\widehat i + 3\widehat j - 3\widehat k$$
B
$$2\widehat i + 3\widehat j + 3\widehat k$$
C
$$-2\widehat i - \widehat j + 5\widehat k$$
D
$$2\widehat i + \widehat j + 5\widehat k$$
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