1
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$\Delta PQR$$ be a triangle. Let $$\vec a = \overrightarrow {QR} ,\vec b = \overrightarrow {RP}$$ and $$\overrightarrow c = \overrightarrow {PQ} .$$ If $$\left| {\overrightarrow a } \right| = 12,\,\,\left| {\overrightarrow b } \right| = 4\sqrt 3 ,\,\,\,\overrightarrow b .\overrightarrow c = 24,$$ then which of the following is (are) true?
A
$${{{{\left| {\overrightarrow c } \right|}^2}} \over 2} - \left| {\overrightarrow a } \right| = 12$$
B
$${{{{\left| {\overrightarrow c } \right|}^2}} \over 2} + \left| {\overrightarrow a } \right| = 30$$
C
$$\left| {\overrightarrow a \times \overrightarrow b + \overrightarrow c \times \overrightarrow a } \right| = 48\sqrt 3$$
D
$$\overrightarrow a .\overrightarrow b = - 72$$
2
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$\overrightarrow x ,\overrightarrow y$$ and $$\overrightarrow z$$ be three vectors each of magnitude $$\sqrt 2$$ and the angle between each pair of them is $${\pi \over 3}$$. If $$\overrightarrow a$$ is a non-zero vector perpendicular to $$\overrightarrow x$$ and $$\overrightarrow y \times \overrightarrow z$$ and $$\overrightarrow b$$ is a non-zero vector perpendicular to $$\overrightarrow y$$ and $$\overrightarrow z \times \overrightarrow x ,$$ then
A
$$\overrightarrow b = \left( {\overrightarrow b \,.\,\overrightarrow z } \right)\left( {\overrightarrow z - \overrightarrow x } \right)$$
B
$$\overrightarrow a = \left( {\overrightarrow a \,.\,\overrightarrow y } \right)\left( {\overrightarrow y - \overrightarrow z } \right)$$
C
$$\overrightarrow a \,.\,\overrightarrow b = - \left( {\overrightarrow a \,.\,\overrightarrow y } \right)\left( {\overrightarrow b \,.\,\overrightarrow z } \right)$$
D
$$\overrightarrow a = -\left( {\overrightarrow a \,.\,\overrightarrow y } \right)\left( {\overrightarrow z - \overrightarrow y } \right)$$
3
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Two lines $${L_1}:x = 5,{y \over {3 - \alpha }} = {z \over { - 2}}$$ and $${L_2}:x = \alpha ,{y \over { - 1}} = {z \over {2 - \alpha }}$$ are coplanar. Then $$\alpha$$ can take value(s)
A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$
4
JEE Advanced 2013 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A line $$l$$ passing through the origin is perpendicular to the lines $$\,{l_1}:\left( {3 + t} \right)\widehat i + \left( { - 1 + 2t} \right)\widehat j + \left( {4 + 2t} \right)\widehat k,\,\,\,\,\, - \infty < t < \infty$$$$${l_2}:\left( {3 + 2s} \right)\widehat i + \left( {3 + 2s} \right)\widehat j + \left( {2 + s} \right)\widehat k,\,\,\,\,\, - \infty < s < \infty$$$
Then, the coordinate(s) of the points(s) on $${l_2}$$ at a distance of $$\sqrt {17}$$ from the point of intersection of $$l$$ and $${l_1}$$ is (are)
A
$$\left( {{7 \over 3},{7 \over 3},{5 \over 3}} \right)$$
B
$$\left( { - 1, - 1,0} \right)$$
C
$$\left( {1,1,1} \right)$$
D
$$\left( {{7 \over 9},{7 \over 9},{8 \over 9}} \right)$$
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