1
IIT-JEE 1999
MCQ (Single Correct Answer)
+2
-0.5
Let $$a=2i+j+k, b=i+2j-k$$ and a unit vector $$c$$ be coplanar. If $$c$$ is perpendicular to $$a,$$ then $$c =$$
A
$${1 \over {\sqrt 2 }}\left( { - j + k} \right)$$
B
$${1 \over {\sqrt 3 }}\left( {- i - j - k} \right)$$
C
$${1 \over {\sqrt 5 }}\left( {i - 2j} \right)$$
D
$${1 \over {\sqrt 3 }}\left( {i - j - k} \right)$$
2
IIT-JEE 1998
MCQ (Single Correct Answer)
+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
$$\alpha = \pm 1,\,\,\beta = 1$$
3
IIT-JEE 1998
MCQ (Single Correct Answer)
+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
$$\left( {u \times v} \right) \bullet w$$
4
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+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
$$\pm \widehat k$$
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