Question

In the diagram below, the vectors ūandv are at
right angles to each other. The length of v is d. The
horizontal and vertical components of ū are a and
b respectively. Find the vertical component of v in
terms of a, b and d.
​

Answer 1

Answer:

ad/√(a² + b²)

Explanation:

In the diagram below, the vectors ūandv are at

right angles to each other. The length of v is d. The

horizontal and vertical components of ū are a and

b respectively. Find the vertical component of v in

terms of a, b and d.

Let say Angle formed by u with base is θ

Then angle formed with vertical by u is 90  - θ

then angle formed by d with base is 180 - 90 - θ = 90  - θ

Angle formed with vertical by v = 90 - (90 - θ) = θ

Hence we can say that these are similar triangles

Let say horizontal of v is x  & vertical is y

x/b  = y/a  = d/√(a² + b²)

=> x = bd/√(a² + b²)

& y = ad/√(a² + b²)

Vertical component of v  is ad/√(a² + b²)