If #hat a# and #hat b# are unit vectors that make an angle of 60 degrees with each other, calculate?

Question

a) #|3hata-5hatb |#
b) #|8hata+3hatb |#

6125 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-11T16:34:11

#sqrt(19)# and #sqrt(97)#

If two vectors #vec"A"# and #vec"B"# are making an angle #θ# then

#|vec"A" + vec"B"| = sqrt("A"^2 + "B"^2 + "2ABcosθ")#
#|vec"A" - vec"B"| = sqrt("A"^2 + "B"^2 - "2ABcosθ")#

Multiplying a vector with positive integer doesn’t change its direction. So,

a)
#|3hata - 5hatb| = sqrt(3^2 + 5^2 - (2 × 3 × 5 × cos60)) = sqrt(19)#

b)
#|8hata + 3hatb| = sqrt(8^2 + 3^2 + (2 × 8 × 3 × cos60)) = sqrt(97)#