Question

F = 40 N at 45°. This vector written in unit vector notation is

❖ᴏɴʟʏ ᴘʀᴏᴘᴇʀ ꜱᴏʟᴠᴇᴅ ᴀɴꜱᴡᴇʀ ᴡɪᴛʜ ɢᴏᴏᴅ ᴇxᴘʟᴀɴᴀɪᴏɴ ɴᴇᴇᴅᴇᴅ
❖ ɴᴏ ꜱᴘᴀᴍᴍɪɴɢ
❖ᴏɴʟʏ ꜰᴏʀ ᴍᴏᴅᴇʀᴀᴛᴏʀꜱ, ʙʀᴀɪɴʟʏ ꜱᴛᴀʀꜱ ᴀɴᴅ ᴏᴛʜᴇʀ ʙᴇꜱᴛ ᴜꜱᴇʀꜱ​​​​​​​​​​​​​​​​​​​​​​​

Answer 1

Given

F=40 N

$\theta = 45^{ \circ}$

$F_x = F \: cos \: 45^{\circ}$

$= \frac{40}{ \sqrt{2} } = 20 \sqrt{2}$

$F_y= F \: sin \: 45^{\circ}$

$= 20 \sqrt{2}$

Thus, unit vector notation is

$\overrightarrow{F}=F_x \hat{i} + F_y \hat{j}$

$= 20 \sqrt{2} ( \hat{i} + \hat{j})$