Two vectors a and b of equal magnitude 5 originating from a point and directs respectively towards north-east and north-west. Then the magnitude of veca- vecb is:

Question

Two vectors a and b of equal magnitude 5 originating from a point and directs respectively towards north-east and north-west. Then the magnitude of veca- vecb is: (A)  3√2  (B)  2√3  (C)  2√5  (D)  5√2

Tardigrade Admin · Accepted Answer

|a-b|2=|a|2+|b |2-2|a||b| cos 90° =25+25-2× 0 =50 ⇒ |a-b|=5√2

Q. Two vectors $a$ and $b$ of equal magnitude 5 originating from a point and directs respectively towards north-east and north-west. Then the magnitude of $a - b$ is:

$32$

$23$

$25$

$52$

$53$

$∣ a - b ∣^{2} = ∣ a ∣^{2} + ∣ b ∣^{2} - 2∣ a ∣∣ b ∣ cos 90^{\circ}$
$= 25 + 25 - 2 \times 0$
$= 50$
$\Rightarrow$ $∣ a - b ∣ = 52$

Q. Two vectors a and b of equal magnitude 5 originating from a point and directs respectively towards north-east and north-west. Then the magnitude of a−b is:

32​

23​

25​

52​

53​

∣a−b∣2=∣a∣2+∣b∣2−2∣a∣∣b∣cos90∘ =25+25−2×0 =50 ⇒ ∣a−b∣=52​