1
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let O be the origin and $$\overrightarrow {OA} = 2\widehat i + 2\widehat j + \widehat k$$ and $$\overrightarrow {OB} = \widehat i - 2\widehat j + 2\widehat k$$ and $$\overrightarrow {OC} = {1 \over 2}\left( {\overrightarrow {OB} - \lambda \overrightarrow {OA} } \right)$$ for some $$\lambda$$ > 0. If $$\left| {\overrightarrow {OB} \times \overrightarrow {OC} } \right| = {9 \over 2}$$, then which of the following statements is (are) TRUE?
A
Projection of $$\overrightarrow {OC} $$ on $$\overrightarrow {OA} $$ is $$ - {3 \over 2}$$
B
Area of the triangle OAB is $${9 \over 2}$$
C
Area of the triangle ABC is $${9 \over 2}$$
D
The acute angle between the diagonals of the parallelogram with adjacent sides $${\overrightarrow {OA} }$$ and $${\overrightarrow {OC} }$$ is $${\pi \over 3}$$
2
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let $$\alpha $$2 + $$\beta $$2 + $$\gamma $$2 $$ \ne $$ 0 and $$\alpha $$ + $$\gamma $$ = 1. Suppose the point (3, 2, $$-$$1) is the mirror image of the point (1, 0, $$-$$1) with respect to the plane $$\alpha $$x + $$\beta $$y + $$\gamma $$z = $$\delta $$. Then which of the following statements is/are TRUE?
A
$$\alpha $$ + $$\beta $$ = 2
B
$$\delta $$ $$-$$ $$\gamma $$ = 3
C
$$\delta $$ + $$\beta $$ = 4
D
$$\alpha $$ + $$\beta $$ + $$\gamma $$ = $$\delta $$
3
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let a and b be positive real numbers. Suppose $$PQ = a\widehat i + b\widehat j$$ and $$PS = a\widehat i - b\widehat j$$ are adjacent sides of a parallelogram PQRS. Let u and v be the projection vectors of $$w = \widehat i + \widehat j$$ along PQ and PS, respectively. If |u| + |v| = |w| and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?
A
a + b = 4
B
a $$-$$ b = 2
C
The length of the diagonal PR of the parallelogram PQRS is 4
D
w is an angle bisector of the vectors PQ and PS
4
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let L1 and L2 be the following straight lines.

$${L_1}:{{x - 1} \over 1} = {y \over { - 1}} = {{z - 1} \over 3}$$ and $${L_2}:{{x - 1} \over { - 3}} = {y \over { - 1}} = {{z - 1} \over 1}$$.

Suppose the straight line

$$L:{{x - \alpha } \over l} = {{y - 1} \over m} = {{z - \gamma } \over { - 2}}$$

lies in the plane containing L1 and L2 and passes through the point of intersection of L1 and L2. If the line L bisects the acute angle between the lines L1 and L2, then which of the following statements is/are TRUE?
A
$$\alpha $$ $$-$$ $$\gamma $$ = 3
B
l + m = 2
C
$$\alpha $$ $$-$$ $$\gamma $$ = 1
D
l + m = 0
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