1
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
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?
A
$$\widehat k$$
B
$$\widehat k$$ + $$\widehat j$$
C
$$\widehat k$$ + $${1 \over 2}$$$$\widehat j$$
D
$$\widehat k$$ $$-$$ $${1 \over 2}$$$$\widehat j$$
2
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
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?
A
$$r = {2 \over 9}(2\widehat i - \widehat j + 2\widehat k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in R$$
B
$$r = {1 \over 3}(2\widehat i + k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in R$$
C
$$r = {2 \over 9}(4\widehat i - \widehat j + \widehat k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in R$$
D
r = $$t(2\widehat i + 2\widehat j - \widehat k)$$, $$t \in R$$
3
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
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?
A
The line of intersection of P1 and P2 has direction ratios 1, 2, $$-$$1
B
The line $${{3x - 4} \over 9} = {{1 - 3y} \over 9} = {z \over 3}$$ is perpendicular to the line of intersection of P1 and P2
C
The acute angle between P1 and P2 is 60$$^\circ $$
D
If P3 is the plane passing through the point (4, 2, $$-$$2) and perpendicular to the line of intersection of P1 and P2, then the distance of the point (2, 1, 1) from the plane P3 is $${2 \over {\sqrt 3 }}$$
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?
A
There is exactly one choice for such $${\overrightarrow v }$$
B
There are infinitely many choices for such $${\overrightarrow v }$$
C
If $$\widehat u$$ lies in the $$xy$$-plane then $$\left| {{u_1}} \right| = \left| {{u_2}} \right|$$
D
If $$\widehat u$$ lies in the $$xz$$-plane then $$2\left| {{u_1}} \right| = \left| {{u_3}} \right|$$
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