Question

Find the magnitude of \(\vec{a}\) and \(\vec{b}\) which are having the same magnitude and such that the angle between them is 60° and their scalar product is \(\frac{1}{4}\).

(a) \(|\vec{a}|=|\vec{b}|=\frac{1}{2√2}\)

(b) \(|\vec{a}|=|\vec{b}|=\frac{1}{√2}\)

(c) \(|\vec{a}|=|\vec{b}|=\frac{1}{2√3}\)

(d) \(|\vec{a}|=|\vec{b}|=\frac{2}{√3}\)

I have been asked this question by my college director while I was bunking the class.

The question is from Product of Two Vectors-2 in portion Vector Algebra of Mathematics – Class 12

Answer 1

Right answer is (a) \(|\vec{a}|=|\vec{b}|=\frac{1}{2√2}\)

The best I can explain: Given that: a) \(|\vec{a}|=|\vec{b}|\)

b) θ=60°

c) \(\vec{a}.\vec{b}=\frac{1}{4}\)

∴\(|\vec{a}||\vec{b}| cos⁡θ=\frac{1}{4}\)

=\(|\vec{a}|^2 cos⁡60°=\frac{1}{4}\)

⇒\(|\vec{a}|^2=\frac{1}{4}.\frac{1}{2}\)

∴\(|\vec{a}|=|\vec{b}|=\frac{1}{2√2}\).