1
AIEEE 2006
+4
-1
The values of a, for which the points $$A, B, C$$ with position vectors $$2\widehat i - \widehat j + \widehat k,\,\,\widehat i - 3\widehat j - 5\widehat k$$ and $$a\widehat i - 3\widehat j + \widehat k$$ respectively are the vertices of a right angled triangle with $$C = {\pi \over 2}$$ are :
A
$$2$$ and $$1$$
B
$$-2$$ and $$-1$$
C
$$-2$$ and $$1$$
D
$$2$$ and $$-1$$
2
AIEEE 2005
+4
-1
If $$C$$ is the mid point of $$AB$$ and $$P$$ is any point outside $$AB,$$ then :
A
$$\overrightarrow {PA} + \overrightarrow {PB} = 2\overrightarrow {PC}$$
B
$$\overrightarrow {PA} + \overrightarrow {PB} = \overrightarrow {PC}$$
C
$$\overrightarrow {PA} + \overrightarrow {PB} = 2\overrightarrow {PC} = \overrightarrow 0$$
D
$$\overrightarrow {PA} + \overrightarrow {PB} = \overrightarrow {PC} = \overrightarrow 0$$
3
AIEEE 2005
+4
-1
Let $$a, b$$ and $$c$$ be distinct non-negative numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\,\,\widehat i + \widehat k$$ and $$c\widehat i + c\widehat j + b\widehat k$$ lie in a plane, then $$c$$ is :
A
the Geometric Mean of $$a$$ and $$b$$
B
the Arithmetic Mean of $$a$$ and $$b$$
C
equal to zero
D
the Harmonic Mean of $$a$$ and $$b$$
4
AIEEE 2005
+4
-1
For any vector $${\overrightarrow a }$$ , the value of $${\left( {\overrightarrow a \times \widehat i} \right)^2} + {\left( {\overrightarrow a \times \widehat j} \right)^2} + {\left( {\overrightarrow a \times \widehat k} \right)^2}$$ is equal to :
A
$$3{\overrightarrow a ^2}$$
B
$${\overrightarrow a ^2}$$
C
$$2{\overrightarrow a ^2}$$
D
$$4{\overrightarrow a ^2}$$
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