question_answer

A vector\[\overset{\to }{\mathop{\text{A}}}\,\] has magnitude 2 and another vector\[\overset{\to }{\mathop{\text{B}}}\,\] has magnitude 3. They are perpendicular to each other. By vector diagram, find the magnitude of \[2\overset{\to }{\mathop{\text{A}}}\,+\overset{\to }{\mathop{\text{B}}}\,\] and show its direction in the diagram.

Answer:

                Draw; \[(\overset{\to }{\mathop{PQ}}\,)=2\overset{\to }{\mathop{\text{A}}}\,\] . Where, PQ = 4 cm; and 1 cm represents, magnitude one, of the given vector. Draw, \[\overset{\to }{\mathop{QS}}\,=\overset{\to }{\mathop{B}}\,\],  perpendicular to \[2\overset{\to }{\mathop{\text{A}}}\,\]. Here, \[QS=3\,cm\].                 Now, \[(2\overset{\to }{\mathop{\text{A}}}\,+\overset{\to }{\mathop{B}}\,)\]will be represented by \[(\overset{\to }{\mathop{PS}}\,)\]. Here,                 \[PS=\sqrt{P{{Q}^{2}}+Q{{S}^{2}}}=\sqrt{{{4}^{2}}+{{3}^{2}}}=5\] Therefore magnitude of \[(2\overset{\to }{\mathop{\text{A}}}\,+\overset{\to }{\mathop{\text{B}}}\,)\]is 5 Fig. 2(c).57.