Grade upto college level Mechanics
Two vectors,![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADQAAAAbCAIAAAC84DtfAAAA1klEQVRYhe2UyxHFIAhFqYuCqIdqbIZikoW+8ROiPEdHM+PZuQgcL0S4NgZWC9Q4cr18W84RkJvVvVHckJwwzvOrFlflHMGDYXp/FP9ecimb79w6FLmwFP5K4YAsA5vma/eeXSEXVkAYAYjjYeBkHcW7+j5WucSxFZf216W8fJ37CGOliy6X3m40jswPkyonjNPcrt9cDB00ucYmBDrHmgvWu2hy84YqjFGnnYEiZwuuC0dJ5SIDYSwzecpNdCtWITcxya0iS9WziZz+0G8ip3PkejlyvdzJ+U7x2FHcfwAAAABJRU5ErkJggg==]()
lie in the xy plane. Their magnitudes are 4.5 and 7.3 units, respectively, whereas their directions are 320° and 85° measured counterclockwise from the positive x axis. What is the value of ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAdCAIAAAC196JdAAAA20lEQVRYhe2U3Q3EIAiAnYuBmIdpWIZhrg+aWKyg2Fx7l/i9mSh+/Gj6/BLpbQHFtrHZNjZ/Y8OYkNcjrxx3ayMEd4TixxsbxnQhEPDm8adqIwQzgo/MjRAk7QUkQZsvkXX6eSqb0va8syyMLEz06HQuPRfKtClNznupLkLNYqz6xq2Mgblx2zpCCwhBG0cI3NitzTm7OIzeixmXurEZyQ8pT7kXY6Lv2sabsLDRQhxtc6dPQlDvX0xL2czFMIZDPZZOWt4/07OZTMixqVwrHLV5n21js21sto3NAeae4patgT5pAAAAAElFTkSuQmCC]()
1 Answer
Navjyot Kalra
Since ϕ is the angle between r and s, so the value of ϕ will be,
Φ = 320̊ - 85̊
= 235̊
Substituting 4.5 units is the magnitude of r and 7.3 units is the magnitude of s and 235̊ for the direction ϕ in the equation r . s = rs cosϕ,
r . s = rs cosϕ
= (4.5) (7.3) cos (235̊)
= -18.84 …… (2)
Rounding off to two significant figures, scalar product of two vectors will be -19.
Φ = 320̊ - 85̊
= 235̊
Substituting 4.5 units is the magnitude of r and 7.3 units is the magnitude of s and 235̊ for the direction ϕ in the equation r . s = rs cosϕ,
r . s = rs cosϕ
= (4.5) (7.3) cos (235̊)
= -18.84 …… (2)
Rounding off to two significant figures, scalar product of two vectors will be -19.
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