Test: Vector Addition: Analytical Method - ACT MCQ

The vector 5 units from the origin and along X axis is 5î. The vector 2 units from the origin and along Y axis is 2ĵ. Hence the sum is 5î + 2ĵ.

The required vector can be obtained by subtracting 40î + 30ĵ from 15î + 3ĵ. The result gives -25î – 27ĵ. One should pay attention on which vector has to be subtracted from which one.

Unit vector along 4î + 3ĵ , is obtained by dividing the present vector by its magnitude. The magnitude of the given vector is 5. Hence, the required unit vector is (4î + 3ĵ)/5.

Consider the graphical representation of these two vectors. When one vector is added to the other in the same direction, the lengths will be added. The resultant vector will bear the resultant length. Length is the magnitude of the vector. Hence the magnitudes add to give the magnitude of the resultant vector.

When 2î + 7ĵ is subtracted from î + ĵ, the corresponding components get subtracted. Hence, the answer is -î – 6ĵ.

Addition of two vectors gives a vector as the result. The same goes for subtraction and cross multiplication. It is only when two vectors are operated through dot product, we get a scalar as the result.

The formula for relative velocity is, Vector V_R = Vector V_A – Vector V_B. Finding relative velocity is an example of vector subtraction. In fact, finding the relative value for any vector quantity, we need to do vector subtraction.

The dot product of any two vectors which are perpendicular to each other is 0. The dot product of all the vectors in the options with 4î + 3ĵ is non-zero except for . Hence  is perpendicular to the given vector.

The vector 7 units from the origin and along X axis is 7î. The vector 11 units from the origin and along Y axis is 11ĵ. Hence the sum is 7î + 11ĵ.

When î + 77ĵ is added to 7î + ĵ, the corresponding components get added. Hence, the answer is 8î + 78ĵ.