If vector $\to P Q$ with coordinates of the end points (1, -2) and (4-1) is equal to vector is with coordinates of initial and final points (a, -1) and (0, 0) respectively, then $| a | =$ ___

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Solution

Two vectors can be said to be equal if they have the same magnitudes and same directions.
Since $- - \to P Q = - - \to R S$
So $∣ ∣ ∣ - - \to P Q ∣ ∣ ∣ = ∣ ∣ ∣ - - \to R S ∣ ∣ ∣$
$∣ ∣ ∣ - - \to P Q ∣ ∣ ∣$ = $\sqrt{(4 - 1)^{2} + (- 1 - (- 2 {))}^{2}}$
= $\sqrt{10}$
Now $∣ ∣ ∣ - - \to R S ∣ ∣ ∣ = \sqrt{(0 - a)^{2} + (0 - (- 1 {))}^{2}}$
= $\sqrt{a^{2} + 1}$
So
$\sqrt{a^{2} + 1} = \sqrt{10}$
or a $^{2}$ + 1 = 10
a $^{2}$ = 9
$\Rightarrow$ a = $\pm$ 3
$\Rightarrow$ $| a | = 3$ .

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