Question

A vector A when added to vector B=3i^+4j^ yields a resultant vector that is in the positive y direction and has a magnitude equal to that if vector B.Find the magnitude of vector A

Answer 1

Let A = x i^ + y j^

resultant, C = A + B = (x + 3) i^ + ( y + 4) j^

but C is in +Y direction.
=> x + 3 = 0
=> x = -3 ............... (1)

since, |C| = |B|
=> |(y+4)j^| = |3 i^ + 4 j^|
=> y + 4 = ✓(3^2 + 4^2)
=> y + 4 = 5
=> y = 1 ......... (2)


now, from (1) and (2)...

A = -3 i^ + j^

|A| = ✓((-3)^2 +1^2) = ✓(9+1) = ✓10 ..... ans ..

Answer 2

Answer: The correct answer is $\sqrt{10}$.

Explanation:

Find the magnitude of B vector B=3i^+4j^ .

$B=\sqrt{3^{2} +4^{2}}$

$B=\sqrt{25}$

$B=5 unit$

It is given in the problem that a resulting vector in the positive y direction and has a magnitude equal to that of vector B. The resulting vector must be equal to 5 j.

R= A+B

A= R-B

A= (0-3)i+(5-4)j

A= -3i+1j

Calculate the magnitude of vector A.

$A=\sqrt{(-3)^{2} +1^{2}}$

$A=\sqrt{10}$

Therefore, the magnitude of vector is $A=\sqrt{10}$.