The magnitude of x and y components of A are 7 and 6 respectively. Also the magnitudes of x and y components of A→+B→ are 11 and 9 respectively. Calculate the magnitude of vector B.

Given A=7ı^+6ȷ^A+B=11ı^+9ȷ^Let, B=b1ı^+b2ȷ^(7ı^+6ȷ^)+(b1ı^+b2ȷ^)=11ı^+9ȷ^ (7ı^+b1)ı^+6+b2)ȷ^=11ı^+9ȷ^ 7+b1 =11⇒b1 =46+b2 =9⇒b2 =3 B=4ı^+3ȷ^ B=42+32=25=5

The magnitude of x and y components of A are 7 and 6 respectively. Also the magnitudes of x and y components of A→+B→ are 11 and 9 respectively. Calculate the magnitude of vector B.

Given A=7ı^+6ȷ^A+B=11ı^+9ȷ^Let, B=b1ı^+b2ȷ^(7ı^+6ȷ^)+(b1ı^+b2ȷ^)=11ı^+9ȷ^ (7ı^+b1)ı^+6+b2)ȷ^=11ı^+9ȷ^ 7+b1 =11⇒b1 =46+b2 =9⇒b2 =3 B=4ı^+3ȷ^ B=42+32=25=5

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The magnitude of x and y components of A are 7 and 6 respectively. Also the magnitudes of x and y components of $\vec{A} + \vec{B}$ are 11 and 9 respectively. Calculate the magnitude of vector B.

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answer is B.

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Detailed Solution

Given $A = 7 \hat{ı} + 6 \hat{ȷ}$

$A + B = 11 \hat{ı} + 9 \hat{ȷ}$

Let, $B = b_{1} \hat{ı} + b_{2} \hat{ȷ}$

$(7 \hat{ı} + 6 \hat{ȷ}) + (b_{1} \hat{ı} + b_{2} \hat{ȷ}) = 11 \hat{ı} + 9 \hat{ȷ} (7 \hat{ı} + b_{1}) \hat{ı} + 6 + b_{2}) \hat{ȷ} = 11 \hat{ı} + 9 \hat{ȷ} \begin{array}{l} 7 + b_{1}^{} = 11 \Rightarrow b_{1}^{} = 4 \\ 6 + b_{2}^{} = 9 \Rightarrow b_{2}^{} = 3 \end{array} B = 4 \hat{ı} + 3 \hat{ȷ} |B| = \sqrt{4^{2} + 3^{2}} = \sqrt{25} = 5$