Question

If θ is the angle between the vectors i + j and j + k, then find sin θ.

Answer 1

Answer:

sin θ = √3/2

Step-by-step explanation:

Angle between two vectors $\vec a,\vec b$ can be calculated by

$cos \theta=\frac{\vec a.\vec b}{|\vec a||\vec b|}$

$\vec a= \hat i+\hat j\\\\\vec b= \hat j+\hat k$

$cos \theta=\frac{1}{\sqrt{2}\sqrt{2}}\\\\\\cos \theta=\frac{1}{2}\\\\\\\theta = cos^{-1} (cos \frac{\pi}{3} )\\\\\theta = \frac{\pi}{3}$

Thus

$sin \;(\frac{\pi}{3}) =\frac{\sqrt{3} }{2}$

Answer 2

Answer:√3/2

hope it's very useful

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