1
IIT-JEE 1998
+2
-0.5
If $$a = i + j + k,\overrightarrow b = 4i + 3j + 4k$$ and $$c = i + \alpha j + \beta k$$ are linearly dependent vectors and $$\left| c \right| = \sqrt 3 ,$$ then
A
$$\alpha = 1,\,\,\beta = - 1$$
B
$$\alpha = 1,\,\,\beta = \pm 1$$
C
$$\alpha = - 1,\,\,\beta = \pm 1$$
D
$$\alpha = \pm 1,\,\,\beta = 1$$
2
IIT-JEE 1998
+2
-0.5
For three vectors $$u,v,w$$ which of the following expression is not equal to any of the remaining three?
A
$$\,u \bullet \left( {v \times w} \right)$$
B
$$\left( {v \times w} \right) \bullet u$$
C
$$\,v \bullet \left( {u \times w} \right)$$
D
$$\left( {u \times v} \right) \bullet w$$
3
IIT-JEE 1995 Screening
+4
-1
Let $$\overrightarrow a = \widehat i - \widehat j,\overrightarrow b = \widehat j - \widehat k,\overrightarrow c = \widehat k - \widehat i.$$ If $$\overrightarrow d$$ is a unit vector such that $$\overrightarrow a .\overrightarrow d = 0 = \left[ {\overrightarrow b \overrightarrow c \overrightarrow d } \right],$$ then $$\overrightarrow d$$ equals
A
$$\pm {{\widehat i + \widehat j - 2k} \over {\sqrt 6 }}$$
B
$$\pm {{\widehat i + \widehat j - k} \over {\sqrt 3 }}$$
C
$$\pm {{\widehat i + \widehat j + k} \over {\sqrt 3 }}$$
D
$$\pm \widehat k$$
4
IIT-JEE 1995 Screening
+4
-1
If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c$$ are non coplanar unit vectors such that $$\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = {{\left( {\overrightarrow b + \overrightarrow c } \right)} \over {\sqrt 2 }},\,\,$$ then the angle between $$\overrightarrow a$$ and $$\overrightarrow b$$ is
A
$${{3\pi } \over 4}$$
B
$${{\pi } \over 4}$$
C
$$\pi /2$$
D
$$\pi$$
EXAM MAP
Medical
NEET