1
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
$$\sqrt {ab}$$
2
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
3
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
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
4
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let a vector $${\overrightarrow a }$$ be coplanar with vectors $$\overrightarrow b = 2\widehat i + \widehat j + \widehat k$$ and $$\overrightarrow c = \widehat i - \widehat j + \widehat k$$. If $${\overrightarrow a}$$ is perpendicular to $$\overrightarrow d = 3\widehat i + 2\widehat j + 6\widehat k$$, and $$\left| {\overrightarrow a } \right| = \sqrt {10}$$. Then a possible value of $$[\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow c } \cr } ] + [\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow d } \cr } ] + [\matrix{ {\overrightarrow a } & {\overrightarrow c } & {\overrightarrow d } \cr } ]$$ is equal to :
A
$$-$$42
B
$$-$$40
C
$$-$$29
D
$$-$$38
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