Question

Vector V⃗ 1 points along the z axis and has magnitude V1 = 76. Vector V⃗ 2 lies in the xz plane, has magnitude V2 = 60, and makes a -48 ∘ angle with the x axis (points below x axis).

What is the scalar product of the two vectors? Express answer using two significant figures.

Answer 1

Answer:

R= - 3388.74

Explanation:

Given that

V₁= 76 k  ( in z-direction)

θ = 48°

V₂ = 60 cos48° i - 60 sin48°  k

The dot product of two vector given as

We know that dot product of two vector  is scalar and cross product of two vector is vector.

R= V₁ . V₂

We have to remember

i.i= j.j = k.k = 1

i.j = j.k = k.i = 0

Now

R= V₁ . V₂

R= (76 k ).(  60 cos48° i - 60 sin48°  k)

R= 0 - 60 x 76  sin48°

R= - 3388.74

Answer 2

The scalar product of the vectors is - 3388.74

Given information:

V₁= 76k  since it is in z-direction

Now vector V₂  makes an angle θ = 48° with x-axis so, it can be resolved as follows:

V₂ = 60 cos48°i - 60 sin48° k

Scalar Product:

The scalar product of vectors is the product of the projection of one vector with the other vector.

The scalar product or the dot product of two vectors is given as

V= V₁ . V₂

The dot product of the x,y,and z direction components follow the below mentioned rule:

i.i= j.j = k.k = 1

i.j = j.k = k.i = 0

So, the required scalar product

V = V₁ . V₂

V = (76k ).(60cos48° i - 60sin48°  k)

V = 0 -60 x 76sin48°

V = - 3388.74

Learn more about scalar product:

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