Question

For what value of M the angle between vector A vector=Mi+j-k and B vector =i+Mj-k is π/3​

Answer 1

Answer:

Angle [math]\theta[/math] between the vectors [math](i+j)[/math] & [math](j+k)[/math] such that [math]0\le \theta\le\pi[/math] is given by dot product as follows

[math](i+j)\cdot (j+k)=i\cdot j+j\cdot j+i\cdot k+j\cdot k[/math]

[math]|i+j||j+k|\cos\theta=1[/math]

[math]\sqrt{2}\sqrt2\cos\theta=1[/math]

[math]2\cos\theta=1[/math]

[math]\cos\theta=\frac12[/math]

[math]\cos \theta=\cos60^\circ[/math]

[math]\theta=60^\circ[/math]