Magnetic field strength is measured using Zeeman splitting. This is the one of the way Sun's magnetic field strength is measured. Now, how one measure vector magnetic field? Vector magnetic field = Magnetic field and it's components.
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$\begingroup$ Look at the flow of plasma. This might help you understand more: nasa.gov/feature/goddard/2016/understanding-the-magnetic-sun $\endgroup$– Kornpob BhirombhakdiCommented Jul 3, 2018 at 13:13
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$\begingroup$ That page again says "Additionally, the footpoints on the sun’s surface, or photosphere, of these magnetic loops can be more precisely measured using an instrument called a magnetograph, which measures the strength and direction of magnetic fields." --- And this was my question too! $\endgroup$– Kartik ChhajedCommented Jul 6, 2018 at 2:11
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$\begingroup$ We scientist use vector magnetogram to extrapolate magnetic field in Sun's Corona and uses phenomena happening on Sun to match the result. What I didn't know was, how do one measure vector magnetogram. Now it's clear. $\endgroup$– Kartik ChhajedCommented Jul 6, 2018 at 2:20
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Using spectropolarimeter one can measure vector Magnetic field.
A spectropolarimeter based on a ferroelectric liquid-crystal modulator is described. An optical system with spatial modulation of the positions of the components of Zeeman splitting is a specific feature of this instrument. In comparison to the familiar instruments, the developed spectropolarimeter utilizes the light flux more efficiently and contains only one photodetector array. An operating spectropolarimeter developed at the Sayan Solar Observatory is considered as an example. Comparative estimates of noises in different operating modes are presented.
(Ref: Kolobov, D.Y., Kobanov, N.I. & Grigoryev, V.M. Instrum Exp Tech (2008) 51: 124. https://doi.org/10.1134/S0020441208010156)