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Bisector of Angle between Two Vectors

If a and b ar...

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{ If }\overline a and }\overline b are non-collinear vectors, then the value of }x for which vectors }\overlineα=(x-2)\overline a+\overline b an }}{\overlineβ=(3+2x)\overline a-2\overline b are collinear, is given by

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¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

are non coplanar vectors and

λ

is a real number, then the vectors

¯ ¯ ¯ a + 2 ¯ ¯ b + 3 ¯ ¯ c, λ ¯ ¯ b + 4 ¯ ¯ c

(2 λ - 1) ¯ ¯ c

are non-coplanar for

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

be three non-zero vectors whcih are pairwise non-collinear. If

¯ ¯ ¯ a + 3 ¯ ¯ b

is collinear with

¯ ¯ c

¯ ¯ b + 2 ¯ ¯ c

is collinear with

¯ ¯ ¯ a

¯ ¯ ¯ a + 3 ¯ ¯ b + 6 ¯ ¯ c

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

be three non-zero vectors, no two of which are collinear. lf the vector

¯ ¯ ¯ a + 2 ¯ ¯ b

is collinear with

¯ ¯ c

¯ ¯ b + 3 ¯ ¯ c

is collinear with

¯ ¯ ¯ a

¯ ¯ ¯ a + ¯ ¯ b + 3 ¯ ¯ c =

Q. Three non-zero non-collinear vectors

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

¯ ¯ ¯ a + 3 ¯ ¯ b

is collinear with

¯ ¯ c

¯ ¯ ¯ 3 b + 2 ¯ ¯ c

is collinear with

¯ ¯ ¯ a

¯ ¯ ¯ a + 3 ¯ ¯ b + 2 ¯ ¯ c =

¯ ¯ ¯ a

¯ ¯ b

are two non-collinear vectors, then the points

l_{1} ¯ ¯ ¯ a + m_{1} ¯ ¯ b

l_{2} ¯ ¯ ¯ a + m_{2} ¯ ¯ b

l_{3} ¯ ¯ ¯ a + m_{3} ¯ ¯ b

are collinear if

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Bisector of Angle between Two Vectors

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