Question

Q. The angle which the
Vector A = 2i + 3j makes with the y - axis , where i and j are unit vector along x - axis and y - axis , respectively , is :-

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$|physics| |class \: \: 11| | \: topic \: vector \: |$

[ Explain whole process and do step by step ]

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[ Be_Brainly ]

Answer 1

Final Answer : tan-1(2/3)

Understanding:
1) Vectors
2) Trigonometry


Steps:
1) We know that angle (a) between two vectors A and B is given by
$\cos(a) = \frac{a.b}{ |a| |b| }$

here(a) and (b) are two vectors.

A = 2i + 3 j
B = unit vector along y - axis = j


2)

$cosa = \frac{(2i + 3j).(j)}{ \sqrt{ {2}^{2} + {3}^{2} } \sqrt{ {1}^{2} } } \\ = > \frac{3}{ \sqrt{13} }$


where a is angle between A and B.

3) Now,
By using trigonometry in triangle,
we get
$\tan(a) = \frac{2}{3}$

From here, angle between A and B a is tan-1(2/3 ) .

Answer 2

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