(a) If \overrightarrow{a} and \overrightarrow{b} are two vectors such that |\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{b}|, then prove that (\overrightarrow{a}+2 \overrightarrow{b}) is perpendicular to \overrightarrow{a}. OR (b) If \overrightarrow{a} and \overrightarrow{b} are unit vectors and \theta is the angle between them, then prove that \sin \frac{\theta}{2}=\frac{1}{2}|\overrightarrow{a}-\overrightarrow{b}|

CBSE Class 12 Math 2022 (Term II) Delhi Set 1 Solved Paper

Question : 8 of 14

Marks: +1, -0

(a) If

{a}↖{→}

and

{b}↖{→}

are two vectors such that

|{a}↖{→}+{b}↖{→}|=|{b}↖{→}|

, then prove that

({a}↖{→}+2 {b}↖{→})

is perpendicular to

{a}↖{→}

.
OR
(b) If

{a}↖{→}

and

{b}↖{→}

are unit vectors and

θ

is the angle between them, then prove that

sin \;\;{θ}/{2}=\;{1}/{2}|{a}↖{→}-{b}↖{→}|

Solution:

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