Question

Vector $\vec{A}$ has components $A_x=2,A_y=3$ and vector $\vec{B}$ has components $B_x=4,B_y=5$, then match the columns:

Column I		Column II
A	The y-components of vector sum $(\vec{A}+\vec{B})$	1	8
B	The magnitude of $\vec{A}+\vec{B}$	2	$-2$
C	The $x$-componet of vector difference $\vec{A}-\vec{B}$	3	$2\sqrt{2}$
D	The magnitude of $(\vec{A}-\vec{B})$	4	10

• A. ( A )$\to$V(1) ; (B) $\to$(4) ; C $\to$ (2) ; (D) $\to$(3)
• B. (A) $\to$ (2); (B) $\to$ (4); C $\to$ (3); (D) $\to$ (1)
• C. (A) $\to$ (3); (B) $\to$ (2); C $\to$ (4); (D) $\to$ (1)
• D. (A) $\to$ (2); (B) $\to$ (4); C $\to$ (1); (D) $\to$ (3)

Answer 1

Answer: (A)

$A\to (1);B\to (4);C\to (2);D\to (3)$
(A) $\vec{A}=2\hat{i}+3\hat{j}$ and $\vec{B}=4\hat{i}+5\hat{j}$
$\therefore \vec{A}+\vec{B}=6\hat{i}+8\hat{j}$
(B) $|\vec{A}+\vec{B}|=\sqrt{6^2+8^2}=10$
(C) $\vec{A}-\vec{B}=(2\hat{i}+3\hat{j})-(4\hat{i}+5\hat{j})=-2\hat{i}-2\hat{j}$
(D) $|\vec{A}-\vec{B}|=\sqrt{(-2{)}^2+(-2{)}^2}=2\sqrt{2}$.