1
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let L1 and L2 denote the lines
$$r = \widehat i + \lambda ( - \widehat i + 2\widehat j + 2\widehat k)$$, $$\lambda $$$$ \in $$ R
and $$r = \mu (2\widehat i - \widehat j + 2\widehat k),\,\mu \in R$$
respectively. If L3 is a line which is perpendicular to both L1 and L2 and cuts both of them, then which of the following options describe(s) L3?
$$r = \widehat i + \lambda ( - \widehat i + 2\widehat j + 2\widehat k)$$, $$\lambda $$$$ \in $$ R
and $$r = \mu (2\widehat i - \widehat j + 2\widehat k),\,\mu \in R$$
respectively. If L3 is a line which is perpendicular to both L1 and L2 and cuts both of them, then which of the following options describe(s) L3?
2
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let P1 : 2x + y $$-$$ z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is(are) TRUE?
3
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$\widehat u = {u_1} \widehat i + {u_2}\widehat j + {u_3}\widehat k$$ be a unit vector in $${{R^3}}$$ and
$$\widehat w = {1 \over {\sqrt 6 }}\left( {\widehat i + \widehat j + 2\widehat k} \right).$$ Given that there exists a vector $${\overrightarrow v }$$ in $${{R^3}}$$ such that $$\left| {\widehat u \times \overrightarrow v } \right| = 1$$ and $$\widehat w.\left( {\widehat u \times \overrightarrow v } \right) = 1.$$ Which of the following statement(s) is (are) correct?
$$\widehat w = {1 \over {\sqrt 6 }}\left( {\widehat i + \widehat j + 2\widehat k} \right).$$ Given that there exists a vector $${\overrightarrow v }$$ in $${{R^3}}$$ such that $$\left| {\widehat u \times \overrightarrow v } \right| = 1$$ and $$\widehat w.\left( {\widehat u \times \overrightarrow v } \right) = 1.$$ Which of the following statement(s) is (are) correct?
4
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Consider a pyramid $$OPQRS$$ located in the first octant $$\left( {x \ge 0,y \ge 0,z \ge 0} \right)$$ with $$O$$ as origin, and $$OP$$ and $$OR$$ along the $$x$$-axis and the $$y$$-axis, respectively. The base $$OPQR$$ of the pyramid is a square with $$OP=3.$$ The point $$S$$ is directly above the mid-point, $$T$$ of diagonal $$OQ$$ such that $$TS=3.$$ Then
Questions Asked from Vector Algebra and 3D Geometry (MCQ (Multiple Correct Answer))
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