Question

The resultant of two vectors `vecA` and `vecB` is `vecC`. If the magnitude of `vecB` is doubled, the new resultant vector becomes perpendicular to `vecA`, then the magnitude of `vecC` is

Options

• 2B

• B

• 3B

• 4B

Answer 1

B

Explanation:

`vecA + vecB = vecC`

C² = A + B + 2AB cos θ  ......(i)

And tan α = `(B sin theta)/(A + B cos theta)`

When B is doubled, resultant is perpendicular to `vecA`

∴ `C_1^2` = A² + 4B² + 4AB cos θ  ......(ii)

From right angled triangle PSR

4B² = `C_1^2 + A^2`

`C_1^2` = 4B² – A²

Substituting in (ii) and solving,

A² + 2AB cos θ = 0  ......(iii)

Substituting (iii) in (i),

C = B