Let a and b be two unit vectors such that |(a + b) + 2(a × b)| = 2. If θ (0, π) is the angle between a and b, then among the statements: (S1): 2| a × b| = | a - b| (S2): The projection of a on (a + b) is 1/2

(C) Both (S1) and (S2) are true.

(D) Both (S1) and (S2) are false.

Vector Algebra: JEE Main 2022 Mathematics question

JEE Main 2022 · 24 Jun, Evening shift · Q5822

JEE Main 202224 Jun, Evening shiftMathematicsMediumVector Algebra184× since 2002

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}