1

JEE Main 2021 (Online) 25th February Evening Shift

Numerical

+4

-1

Let $$\overrightarrow a = \widehat i + \alpha \widehat j + 3\widehat k$$ and $$\overrightarrow b = 3\widehat i - \alpha \widehat j + \widehat k$$. If the area of the parallelogram whose adjacent sides are represented by the vectors $$\overrightarrow a $$ and $$\overrightarrow b $$ is $$8\sqrt 3 $$ square units, then $$\overrightarrow a $$ . $$\overrightarrow b $$ is equal to __________.

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2

JEE Main 2021 (Online) 25th February Morning Shift

Numerical

+4

-1

Let $$\overrightarrow a = \widehat i + 2\widehat j - \widehat k$$, $$\overrightarrow b = \widehat i - \widehat j$$ and $$\overrightarrow c = \widehat i - \widehat j - \widehat k$$ be three given vectors. If $$\overrightarrow r $$ is a vector such that $$\overrightarrow r \times \overrightarrow a = \overrightarrow c \times \overrightarrow a $$ and $$\overrightarrow r .\,\overrightarrow b = 0$$, then $$\overrightarrow r .\,\overrightarrow a $$ is equal to __________.

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3

JEE Main 2021 (Online) 24th February Morning Shift

Numerical

+4

-1

Out of Syllabus

Let three vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be such that $$\overrightarrow c $$ is coplanar

with $$\overrightarrow a $$ and $$\overrightarrow b $$, $$\overrightarrow a .\overrightarrow c $$ = 7 and $$\overrightarrow b $$ is perpendicular to $$\overrightarrow c $$, where

$$\overrightarrow a = - \widehat i + \widehat j + \widehat k$$ and $$\overrightarrow b = 2\widehat i + \widehat k$$ , then the

value of $$2{\left| {\overrightarrow a + \overrightarrow b + \overrightarrow c } \right|^2}$$ is _____.

with $$\overrightarrow a $$ and $$\overrightarrow b $$, $$\overrightarrow a .\overrightarrow c $$ = 7 and $$\overrightarrow b $$ is perpendicular to $$\overrightarrow c $$, where

$$\overrightarrow a = - \widehat i + \widehat j + \widehat k$$ and $$\overrightarrow b = 2\widehat i + \widehat k$$ , then the

value of $$2{\left| {\overrightarrow a + \overrightarrow b + \overrightarrow c } \right|^2}$$ is _____.

Your input ____

4

JEE Main 2020 (Online) 6th September Evening Slot

Numerical

+4

-0

If $$\overrightarrow x $$ and $$\overrightarrow y $$ be two non-zero vectors such that
$$\left| {\overrightarrow x + \overrightarrow y } \right| = \left| {\overrightarrow x } \right|$$ and $${2\overrightarrow x + \lambda \overrightarrow y }$$ is perpendicular to $${\overrightarrow y }$$,
then the value of $$\lambda $$ is _________ .

Your input ____

Questions Asked from Vector Algebra (Numerical)

Number in Brackets after Paper Indicates No. of Questions

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