Find the unit vector parallel to the resultant of two vectors a → = i ^ + 4 j ^ + k ^ and b → = 3 i ^ - 5 j ^ + k ^ .

Given a → = i ^ + 4 j ^ + k ^ and b → = 3 i ^ - 5 j ^ + k ^ The sum of the two vectors is a → + b → = i ^ + 4 j ~ + k ~ + 3 i ^ - 5 j ^ + k ^ = i 1 + 3 + j 4 - 5 + k 1 + 1 = 4 i ^ - j ^ + 2 k ^ Now sum of their magnitudes is= a → + b → = 4 2 + - 1 2 + 2 2 = 21 The unit vectors is given by: a → + b → a → + b → = 1 21 4 i ^ - j ^ + 2 k ^

Find the unit vector parallel to the resultant of two vectors a → = i ^ + 4 j ^ + k ^ and b → = 3 i ^ - 5 j ^ + k ^ .

Given a → = i ^ + 4 j ^ + k ^ and b → = 3 i ^ - 5 j ^ + k ^ The sum of the two vectors is a → + b → = i ^ + 4 j ~ + k ~ + 3 i ^ - 5 j ^ + k ^ = i 1 + 3 + j 4 - 5 + k 1 + 1 = 4 i ^ - j ^ + 2 k ^ Now sum of their magnitudes is= a → + b → = 4 2 + - 1 2 + 2 2 = 21 The unit vectors is given by: a → + b → a → + b → = 1 21 4 i ^ - j ^ + 2 k ^

Find a unit vector perpendicular to each of the vectors A → = 3 i ^ + 2 j ^ - k ^ and B → = i ^ + j ^ + k ^

Given the two vectors A → = 3 i ^ + 2 j ^ - k ^ , and B → = i ^ + j ^ + k ^ We know that the cross product of any two vectors yields a vector that is perpendicular to both vectors. The cross product of the vectors is: A → × B → = i ^ j ^ k ^ 3 2 - 1 1 1 1 = i ^ 2 - - 1 - j ^ 3 - - 1 + k ^ 3 - 2 = 3 i ^ - 4 j ^ + k ^ The magnitude of this vector is A → + B → = 3 2 + 4 2 + 1 2 = 26 The unit vector of the vector is given by : A → × B → A → × B → = 1 26 3 i ^ - 4 j ^ + k ^

A B C is a triangle and A D is the median. A D and D C represent the vectors P → and Q → . What are the vectors represented by A C .

. Given A triangle ABC and AD is the media AD = P → and D C = Q → AC = ? Consider the triangle ADC Applying the law of triangular law of vector addition, The side AC is the third side of the triangle ADC , Therefore, we have A D → + D C → = A C → or we can say A C → = P → + Q →

A B C is a triangle and A D is the median. A D and D C represent the vectors P → and Q → . What are the vectors represented by B D .?

. Given A triangle ABC and AD is the median AD = P → and D C = Q → D C → = ? Consider the triangle AD B Since A D is a median, the side BD = DC Since the side D C = P → and side B D is equal to D C in opposite direction, it will represent an equal vector in opposite direction, Therefore, we have , B D = - Q →

A B C is a triangle and A D is the median. A D and D C represent the vectors P → and Q → . What are the vectors represented by B C .?

. Given A triangle ABC and AD is the median AD = P → and D C = Q → B C = ? As A D is median on B C , hence, BD = DC . Therefore, we can say that at point D , two equal and opposite colinear vectors are operating. Therefore, there vector sum will be zero. Hence, we can say B C → = 0 or it is a null vector.

A B C is a triangle and A D is the median. A D and D C represent the vectors P → and Q → . What are the vectors represented by A B ?

. . Given A triangle ABC and AD is the median, AD = P → and D C = Q → AB = ? Consider the triangle ADB Applying the law of triangular law of vector addition, The side AB is the third side of the triangle ADB , Therefore, we have, A D → + D B → = A B → Since AD is perpendicular bisector of BC , therefore BD = DC . Since DC = Q → and BD is equal and opposite to it, hence BD = - Q Applying the law of triangular addition of the vector to the triangle ABD , we have, AB = AD + DB = P → + ( - Q → ) = P → - Q →