Question

What is the resolved form for a vector which is 5 units in long and is inclined at an angle of 45 degrees to the X axis?

(a) \(\frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{2}}\hat{j}\)

(b) \(\frac{5}{\sqrt{2}}\hat{i} + \frac{5}{\sqrt{2}}\hat{j}\)

(c) \(\frac{5}{\sqrt{2}}\hat{i} + \frac{15}{\sqrt{2}}\hat{j}\)

(d) \(\frac{10}{\sqrt{2}}\hat{i} + \frac{10}{\sqrt{2}}\hat{j}\)

I have been asked this question in my homework.

Question is from Motion in a Plane topic in division Motion in a Plane of Physics – Class 11

Answer 1

Right option is (b) \(\frac{5}{\sqrt{2}}\hat{i} + \frac{5}{\sqrt{2}}\hat{j}\)

To explain I would say: The standard for is a(cos θ î + sin θ ĵ). Here, a = 5, and θ = 45 degrees. When we substitute this in the equation, we get, the resolved vector as \(\frac{5}{\sqrt{2}}\hat{i} + \frac{5}{\sqrt{2}}\hat{j}\).