1
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
$$5(30\widehat i - 5\widehat j + 7\widehat k)$$
2
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
$$\sqrt {ab}$$
3
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
If $$\left| {\overrightarrow a } \right| = 2,\left| {\overrightarrow b } \right| = 5$$ and $$\left| {\overrightarrow a \times \overrightarrow b } \right|$$ = 8, then $$\left| {\overrightarrow a .\,\overrightarrow b } \right|$$ is equal to :
A
6
B
4
C
3
D
5
4
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Out of Syllabus
Let the vectors

$$(2 + a + b)\widehat i + (a + 2b + c)\widehat j - (b + c)\widehat k,(1 + b)\widehat i + 2b\widehat j - b\widehat k$$ and $$(2 + b)\widehat i + 2b\widehat j + (1 - b)\widehat k$$, $$a,b,c, \in R$$

be co-planar. Then which of the following is true?
A
2b = a + c
B
3c = a + b
C
a = b + 2c
D
2a = b + c
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