the angle that vector a=2icap+3jcap makes with y axis

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Solution

$\vec{a} = 2 \overset{⏜}{i} + 3 \overset{⏜}{j} M a g n i t u d e o f \vec{a} = |\vec{a}| = \sqrt{4 + 9} = \sqrt{13} t a k i n g d o t p r o d u c t w i t h y - a x i s w e g e t \vec{a} . \overset{⏜}{j} = |\vec{a}| |\overset{⏜}{j}| \cos θ w h e r e θ i s t h e a n g l e m a d e b y t h e v e c t o r a w i t h y a x i s 3 = \sqrt{13} \cos θ θ = \cos^{- 1} (\frac{3}{\sqrt{13}})$

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the angle that vector a=2icap+3jcap makes with y axis

a→ = 2i⏜ + 3j⏜ Magnitude of a→ = a→ = 4+9 = 13taking dot product with y - axiswe geta→ .j⏜ = a→ j⏜ cos θwhere θ is the angle made by the vector a with y axis3 = 13 cos θθ = cos-1(313)