Resultant of 2 vectors P & Q is inclined at 45 to either of them. What is the magnitude of resultant vector?

If P+Q makes a 45° angle with both P and Q, then P must be perpendicular to Q.

So, |P+Q| = √(|P|^2 + |Q|^2)

Good

To find the magnitude of the resultant vector, you can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Let's assume that the magnitude of vector P is represented by |P| and the magnitude of vector Q is represented by |Q|. Since the resultant vector is inclined at 45 degrees to either of them, the triangle formed between P, Q, and the resultant vector is a right triangle.

According to the Pythagorean theorem, the magnitude of the resultant vector (R) can be calculated as follows:

R^2 = P^2 + Q^2

Since the vectors are inclined at 45 degrees, we can assume that they have equal magnitudes, so |P| = |Q|. Thus, we can rewrite the equation as:

R^2 = 2P^2

To find the magnitude of the resultant vector, we need to take the square root of both sides:

R = √(2P^2)

Therefore, the magnitude of the resultant vector, R, is √(2P^2).

To find the magnitude of the resultant vector, we need to use vector addition. Let's denote vector P as P and vector Q as Q.

If the resultant vector is inclined at 45 degrees to either vector P or vector Q, then it forms a right angle triangle. The magnitudes of vector P and vector Q can be represented as the lengths of the two sides of the triangle.

Using the Pythagorean theorem, the magnitude of the resultant vector can be calculated using the formula:

Resultant magnitude = √(P^2 + Q^2)

So, to find the magnitude of the resultant vector, you need to know the magnitudes of vectors P and Q, and then compute the square root of the sum of their squares.