1
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k$$ and $$\overrightarrow b = \widehat j - \widehat k$$. If $$\overrightarrow c$$ is a vector such that $$\overrightarrow a \times \overrightarrow c = \overrightarrow b$$ and $$\overrightarrow a .\overrightarrow c = 3$$, then $$\overrightarrow a .(\overrightarrow b \times \overrightarrow c )$$ is equal to :
A
$$-$$2
B
$$-$$6
C
6
D
2
2
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Let $$\overrightarrow a$$, $$\overrightarrow b$$ and $$\overrightarrow c$$ be three vectors such that $$\overrightarrow a$$ = $$\overrightarrow b$$ $$\times$$ ($$\overrightarrow b$$ $$\times$$ $$\overrightarrow c$$). If magnitudes of the vectors $$\overrightarrow a$$, $$\overrightarrow b$$ and $$\overrightarrow c$$ are $$\sqrt 2$$, 1 and 2 respectively and the angle between $$\overrightarrow b$$ and $$\overrightarrow c$$ is $$\theta \left( {0 < \theta < {\pi \over 2}} \right)$$, then the value of 1 + tan$$\theta$$ is equal to :
A
$$\sqrt 3 + 1$$
B
2
C
1
D
$${{\sqrt 3 + 1} \over {\sqrt 3 }}$$
3
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Let $$\overrightarrow a = \widehat i + \widehat j + 2\widehat k$$ and $$\overrightarrow b = - \widehat i + 2\widehat j + 3\widehat k$$. Then the vector product $$\left( {\overrightarrow a + \overrightarrow b } \right) \times \left( {\left( {\overrightarrow a \times \left( {\left( {\overrightarrow a - \overrightarrow b } \right) \times \overrightarrow b } \right)} \right) \times \overrightarrow b } \right)$$ is equal to :
A
$$5(34\widehat i - 5\widehat j + 3\widehat k)$$
B
$$7(34\widehat i - 5\widehat j + 3\widehat k)$$
C
$$7(30\widehat i - 5\widehat j + 7\widehat k)$$
D
$$5(30\widehat i - 5\widehat j + 7\widehat k)$$
4
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
Let a, b and c be distinct positive numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\widehat i+\widehat k$$ and $$c\widehat i + c\widehat j + b\widehat k$$ are co-planar, then c is equal to :
A
$${2 \over {{1 \over a} + {1 \over b}}}$$
B
$${{a + b} \over 2}$$
C
$${1 \over a} + {1 \over b}$$
D
$$\sqrt {ab}$$
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