Question

the scalar product of two vectors 5N and 2N is 5N , angle between them is; A.60 B.90 C.30 D.none plz explain it clearly

Answer 1

GiveN :

• Scalar Product is 5
• Vectors are : 2N and 5N

To FinD :

• Angle between the vectors

SolutioN :

• Let, First Vector $\sf{F_1 \: = \: 5N}$

• Second Vector $\sf{F_2 \: = \: 2N}$

• Scalar Product $\sf{F_{net} \: = \: 5N}$

$\longrightarrow \boxed{\sf{F_{net} \: = \: F_1 . F_2 }}$

$\longrightarrow \sf{F_{net} \: = \: F_1 . F_2 \cos \theta}$

$\longrightarrow \sf{5 \: = \: 5 \: \times \: 2 \: \times \: \cos \theta}$

$\longrightarrow \sf{5 \: = \: 10 \cos \theta}$

$\longrightarrow \sf{\cos \theta \: = \: \dfrac{10}{5}}$

$\longrightarrow \sf{\cos \theta \: = \: \dfrac{1}{2}}$

$\longrightarrow \sf{\theta \: = \: \cos ^{-1} \bigg( \dfrac{1}{2} \bigg)}$

$\longrightarrow \sf{\theta \: = \: 60^{\circ}}$

$\underline{\underline{\sf{Angle \: between \: vectors \: is \: 60^{\circ}}}}$

Answer 2

Given ,

• The scalar product of two vectors 5 N and 2 N is 5 N

We know that , the scalar product of two vectors A and B is given by

$\boxed{ \sf \vec{A}.\vec{B} = ABcos( \theta)}$

Thus ,

$\mapsto \sf 5 = 2 \times 5 \times cos( \theta) \\ \\\mapsto \sf 5 = 10 \times cos( \theta) \\ \\ \mapsto \sf cos( \theta) = \frac{1}{2} \\ \\ \mapsto \sf ( \theta) = 60$

$\sf \therefore \underline{The \: angle \: between \: two \: vectors \: is \: 60}$