Doubt in attached image

Asked by agarwalakshat2705 | 12th Jun, 2021, 12:04: PM

Expert Answer:

Let us consider two vectors A and B as shown in figure . Let θ be the angle between them . 
 
By cosine formula, magnitude of sum vector is given as
 
begin mathsize 14px style open vertical bar A with rightwards arrow on top space plus space B with rightwards arrow on top close vertical bar space equals space square root of open vertical bar A with rightwards arrow on top close vertical bar squared space plus open vertical bar B with rightwards arrow on top close vertical bar squared space minus space 2 space open vertical bar A with rightwards arrow on top close vertical bar space open vertical bar B with rightwards arrow on top close vertical bar space cos theta end root end style .....................(1)
when θ = π , we get  , begin mathsize 14px style open vertical bar A with rightwards arrow on top space plus space B with rightwards arrow on top close vertical bar space equals space vertical line A with rightwards arrow on top vertical line space plus space vertical line B with rightwards arrow on top vertical line end style  ........................ (2)
Hence if two vectors A and B satisfies above condition (2) , then angle θ between the vectors is given as , θ = π

Answered by Thiyagarajan K | 12th Jun, 2021, 12:45: PM