If-k-is-any-possible-number-what-is-the-size-of-angle-between-the-vectors-a-K-k-and-b-3-4-

Question Number 18284 by tawa tawa last updated on 18/Jul/17

If k is any possible number . what is the size of angle between the vectors

a (K, k) and b (- 3, 4)

Answered by Arnab Maiti last updated on 18/Jul/17

let \vec{A} = K \hat{i} + k \hat{j}

\vec{B} = - 3 \hat{i} + 4 \hat{j}

\vec{A} . \vec{B} = - 3 K + 4 k

\vec{B} . \vec{B} = B^{2} = 9 + 16 = 25

B = 5

\vec{A} . \vec{A} = A^{2} = K^{2} + k^{2}

A = \sqrt{K^{2} + k^{2}}

\vec{A} . \vec{B} = ABcos θ

\cos θ = \frac{- 3 K + 4 k}{5 \sqrt{K^{2} + k^{2}}}

θ = \cos^{- 1} (\frac{- 3 K + 4 k}{5 \sqrt{K^{2} + k^{2}}})

Commented by tawa tawa last updated on 18/Jul/17

God bless you sir .