1
AIEEE 2004
+4
-1
A particle acted on by constant forces $$4\widehat i + \widehat j - 3\widehat k$$ and $$3\widehat i + \widehat j - \widehat k$$ is displaced from the point $$\widehat i + 2\widehat j + 3\widehat k$$ to the point $$\,5\widehat i + 4\widehat j + \widehat k.$$ The total work done by the forces is
A
$$50$$ units
B
$$20$$ units
C
$$30$$ units
D
$$40$$ units
2
AIEEE 2004
+4
-1
Let $$\overrightarrow u ,\overrightarrow v ,\overrightarrow w$$ be such that $$\left| {\overrightarrow u } \right| = 1,\,\,\,\left| {\overrightarrow v } \right|2,\,\,\,\left| {\overrightarrow w } \right|3.$$ If the projection $${\overrightarrow v }$$ along $${\overrightarrow u }$$ is equal to that of $${\overrightarrow w }$$ along $${\overrightarrow u }$$ and $${\overrightarrow v },$$ $${\overrightarrow w }$$ are perpendicular to each other then $$\left| {\overrightarrow u - \overrightarrow v + \overrightarrow w } \right|$$ equals
A
$$14$$
B
$${\sqrt {7} }$$
C
$${\sqrt {14} }$$
D
$$2$$
3
AIEEE 2004
+4
-1
If $${\overrightarrow a ,\overrightarrow b ,\overrightarrow c }$$ are non-coplanar vectors and $$\lambda$$ is a real number, then the vectors $${\overrightarrow a + 2\overrightarrow b + 3\overrightarrow c ,\,\,\lambda \overrightarrow b + 4\overrightarrow c }$$ and $$\left( {2\lambda - 1} \right)\overrightarrow c$$ are non coplanar for
A
no value of $$\lambda$$
B
all except one value of $$\lambda$$
C
all except two values of $$\lambda$$
D
all values of $$\lambda$$
4
AIEEE 2004
+4
-1
Let $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ be non-zero vectors such that $$\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c = {1 \over 3}\left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right|\overrightarrow a \,\,.$$ If $$\theta$$ is the acute angle between the vectors $${\overrightarrow b }$$ and $${\overrightarrow c },$$ then $$sin\theta$$ equals
A
$${{2\sqrt 2 } \over 3}$$
B
$${{\sqrt 2 } \over 3}$$
C
$${2 \over 3}$$
D
$${1 \over 3}$$
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