1
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Three lines $${L_1}:r = \lambda \widehat i$$, $$\lambda $$ $$ \in $$ R,
$${L_2}:r = \widehat k + \mu \widehat j$$, $$\mu $$ $$ \in $$ R and
$${L_3}:r = \widehat i + \widehat j + v\widehat k$$, v $$ \in $$ R are given.
For which point(s) Q on L2 can we find a point P on L1 and a point R on L3 so that P, Q and R are collinear?
$${L_2}:r = \widehat k + \mu \widehat j$$, $$\mu $$ $$ \in $$ R and
$${L_3}:r = \widehat i + \widehat j + v\widehat k$$, v $$ \in $$ R are given.
For which point(s) Q on L2 can we find a point P on L1 and a point R on L3 so that P, Q and R are collinear?
2
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?
3
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?
4
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?
Questions Asked from Vector Algebra and 3D Geometry (MCQ (Multiple Correct Answer))
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