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1
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let L be the line of intersection of planes $$\overrightarrow r .(\widehat i - \widehat j + 2\widehat k) = 2$$ and $$\overrightarrow r .(2\widehat i + \widehat j - \widehat k) = 2$$. If $$P(\alpha ,\beta ,\gamma )$$ is the foot of perpendicular on L from the point (1, 2, 0), then the value of $$35(\alpha + \beta + \gamma )$$ is equal to :
A
101
B
119
C
143
D
134
2
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+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
3
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let three vectors $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\overrightarrow c $$ be such that $$\overrightarrow a \times \overrightarrow b = \overrightarrow c $$, $$\overrightarrow b \times \overrightarrow c = \overrightarrow a $$ and $$\left| {\overrightarrow a } \right| = 2$$. Then which one of the following is not true?
A
$$\overrightarrow a \times \left( {(\overrightarrow b + \overrightarrow c ) \times (\overrightarrow b \times \overrightarrow c )} \right) = \overrightarrow 0 $$
B
Projection of $$\overrightarrow a $$ on $$(\overrightarrow b \times \overrightarrow c )$$ is 2
C
$$\left[ {\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow c } \cr } } \right] + \left[ {\matrix{ {\overrightarrow c } & {\overrightarrow a } & {\overrightarrow b } \cr } } \right] = 8$$
D
$${\left| {3\overrightarrow a + \overrightarrow b - 2\overrightarrow c } \right|^2} = 51$$
4
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
If the shortest distance between the straight lines $$3(x - 1) = 6(y - 2) = 2(z - 1)$$ and $$4(x - 2) = 2(y - \lambda ) = (z - 3),\lambda \in R$$ is $${1 \over {\sqrt {38} }}$$, then the integral value of $$\lambda$$ is equal to :
A
3
B
2
C
5
D
$$-$$1
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