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1
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
Let a vector $$\alpha \widehat i + \beta \widehat j$$ be obtained by rotating the vector $$\sqrt 3 \widehat i + \widehat j$$ by an angle 45$$^\circ$$ about the origin in counterclockwise direction in the first quadrant. Then the area of triangle having vertices ($$\alpha$$, $$\beta$$), (0, $$\beta$$) and (0, 0) is equal to :
A
$${1 \over {\sqrt 2 }}$$
B
$${1 \over 2}$$
C
1
D
2$${\sqrt 2 }$$
2
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
Let the position vectors of two points P and Q be 3$$\widehat i$$ $$-$$ $$\widehat j$$ + 2$$\widehat k$$ and $$\widehat i$$ + 2$$\widehat j$$ $$-$$ 4$$\widehat k$$, respectively. Let R and S be two points such that the direction ratios of lines PR and QS are (4, $$-$$1, 2) and ($$-$$2, 1, $$-$$2), respectively. Let lines PR and QS intersect at T. If the vector $$\overrightarrow {TA}$$ is perpendicular to both $$\overrightarrow {PR}$$ and $$\overrightarrow {QS}$$ and the length of vector $$\overrightarrow {TA}$$ is $$\sqrt 5$$ units, then the modulus of a position vector of A is :
A
$$\sqrt {171}$$
B
$$\sqrt {227}$$
C
$$\sqrt {482}$$
D
$$\sqrt {5}$$
3
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
Let P be a plane lx + my + nz = 0 containing

the line, $${{1 - x} \over 1} = {{y - 4} \over 2} = {{z + 2} \over 3}$$. If plane P divides the line segment AB joining

points A($$-$$3, $$-$$6, 1) and B(2, 4, $$-$$3) in ratio k : 1 then the value of k is equal to :
A
2
B
3
C
1.5
D
4
4
JEE Main 2021 (Online) 16th March Morning Shift
If for a > 0, the feet of perpendiculars from the points A(a, $$-$$2a, 3) and B(0, 4, 5) on the plane lx + my + nz = 0 are points C(0, $$-$$a, $$-$$1) and D respectively, then the length of line segment CD is equal to:
$$\sqrt {41}$$
$$\sqrt {55}$$
$$\sqrt {31}$$
$$\sqrt {66}$$