Question

a, b and c are unit vectors such that a + b - c = 0, then what will be the angle between a and b?

Answer 1

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name Harshit ..
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Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

ᴀ, ʙ ᴀɴᴅ ᴄ ᴀʀᴇ ᴜɴɪᴛ ᴠᴇᴄᴛᴏʀꜱ ꜱᴜᴄʜ ᴛʜᴀᴛ ᴀ + ʙ - ᴄ = 0, ᴛʜᴇɴ ᴡʜᴀᴛ ᴡɪʟʟ ʙᴇ ᴛʜᴇ ᴀɴɢʟᴇ ʙᴇᴛᴡᴇᴇɴ ᴀ ᴀɴᴅ ʙ?

♣ ᴀɴꜱᴡᴇʀ:

$\vec{a}+b=-\vec{c}$

$\Rightarrow|\vec{a}+\vec{b}|^{2}=|\vec{c}|^{2}=1$

$\Rightarrow|\vec{a}|^{2}+|\vec{b}|^{2}+2 \vec{a} \cdot \vec{b}=1$

$\Rightarrow \vec{a} \cdot \vec{b}=-\dfrac{1}{2}$

$\Rightarrow|\vec{a}||\vec{b}| \cos \theta=-\dfrac{1}{2}$

$\Rightarrow \cos \theta=-\dfrac{1}{2}$