Question

If two vectors of magnitude of 5 and 3 are added such that angle between resultant and vector of magnitude 5 is maximum that it will be

Answer 1

Answer:

The angle between resultant and vector of magnitude $5$ is maximum will be $-\frac{5}{3}$

Explanation:

Given that if two vectors of the  magnitude of $5$ and $3$ are added such that the angle between the  resultant and vector of magnitude is $5$

Now $tan\alpha$ is maximum as maximum value is infinity.

$tan\alpha=\frac{A Sin\theta}{B. A cos\theta}$

Now the maximum value is infinity then the denominator should be zero.

$B.A cos\theta=0\\Acos \theta= -B\\cos\theta=-\frac{B}{A} \\cos\theta = -\frac{5}{3}$

Answer 2

Answer:

The angle will be cos⁻¹(-5/3).

Explanation:

Given:

Magnitude of vector A = 3

Magnitude of vector B = 5

To find:

The angle between the resultant and vector of magnitude 5 (α) =?

Formula:

tan(α) = (Asinθ)/(B+Acosθ)

Solution:

It is given that the angle between the resultant and the vector is maximum.

We know that tanθ has a maximum value of infinity. Therefore,

tan(α) = (Asinθ)/(B+Acosθ) = ∞

For the fraction to be infinity, the denominator must be zero. Hence,

B+Acosθ = 0

Acosθ = -B

cosθ = -B/A

Substituting the values of A and B, we get

cosθ = -5/3

θ = cos⁻¹(-5/3)

Therefore, the angle between the resultant and the vector of magnitude 5 is cos⁻¹(-5/3).

#SPJ3