1
AIEEE 2008
+4
-1
Out of Syllabus
The vector $$\overrightarrow a = \alpha \widehat i + 2\widehat j + \beta \widehat k$$ lies in the plane of the vectors
$$\overrightarrow b = \widehat i + \widehat j$$ and $$\overrightarrow c = \widehat j + \widehat k$$ and bisects the angle between $$\overrightarrow b$$ and $$\overrightarrow c$$.Then which one of the following gives possible values of $$\alpha$$ and $$\beta$$ ?
A
$$\alpha = 2,\,\,\beta = 2$$
B
$$\alpha = 1,\,\,\beta = 2$$
C
$$\alpha = 2,\,\,\beta = 1$$
D
$$\alpha = 1,\,\,\beta = 1$$
2
AIEEE 2008
+4
-1
The non-zero vectors are $${\overrightarrow a ,\overrightarrow b }$$ and $${\overrightarrow c }$$ are related by $${\overrightarrow a = 8\overrightarrow b }$$ and $${\overrightarrow c = - 7\overrightarrow b \,\,.}$$ Then the angle between $${\overrightarrow a }$$ and $${\overrightarrow c }$$ is :
A
$$0$$
B
$${\pi \over 4}$$
C
$${\pi \over 2}$$
D
$$\pi$$
3
AIEEE 2007
+4
-1
If $$\widehat u$$ and $$\widehat v$$ are unit vectors and $$\theta$$ is the acute angle between them, then $$2\widehat u \times 3\widehat v$$ is a unit vector for :
A
no value of $$\theta$$
B
exactly one value of $$\theta$$
C
exactly two values of $$\theta$$
D
more than two values of $$\theta$$
4
AIEEE 2007
+4
-1
Out of Syllabus
Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow b = \widehat i - \widehat j + 2\widehat k$$ and $$\overrightarrow c = x\widehat i + \left( {x - 2} \right)\widehat j - \widehat k\,\,.$$ If the vectors $$\overrightarrow c$$ lies in the plane of $$\overrightarrow a$$ and $$\overrightarrow b$$, then $$x$$ equals :
A
$$-4$$
B
$$-2$$
C
$$0$$
D
$$1.$$
EXAM MAP
Medical
NEET