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Vector Algebra question

2022 · 24 Jun · Shift 2 · Q34

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JEE Main
Mathematics
Vector Algebra
2022 · 24 Jun · Shift 2 · Q34

Vector Algebra question

2022 · 24 Jun · Shift 2 · Q34

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\widehat a

and

\widehat b

be two unit vectors such that

|(\widehat a + \widehat b) + 2(\widehat a \times \widehat b)| = 2

. If

\theta\in

(0,

\pi

) is the angle between

\widehat a

and

\widehat b

, then among the statements : (S1) :

2|\widehat a \times \widehat b| = |\widehat a - \widehat b|

(S2) : The projection of

\widehat a

on (

\widehat a

+

\widehat b

) is

{1 \over 2}

A
Only (S1) is true.
B
Only (S2) is true.
C
Both (S1) and (S2) are true.
D
Both (S1) and (S2) are false.

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