When two vectors- a- and b- are added- the magnitude of the resultant vector is alwaysA- less than - a - b -B- equal to - a - b -C- less than or equal to -a-b-D- Greater than - a - b -

The correct option is C less than or equal to (|a| + |b|) nbsp; We know that, |a| + |b| ≥ |a + b| gt; |a| |b| Hence, the magnitude of resultant vector ...

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Byju's Answer

Standard XII

Physics

Vector Addition

When two vect...

Question

When two vectors, $\to a$ and $\to b$ are added, the magnitude of the resultant vector is always

Greater than

(| \to a | + | \to b |)

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less than or equal to

(| \to a | + | \to b |)

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less than

(| \to a | + | \to b |)

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equal to

(| \to a | + | \to b |)

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Solution

Step 1: Given that:
Two vectors $\to a$ and $\to b$ are added, that is $\to a + \to b$ .
Step 2: Finding the nature of the resultant:
When two vectors are added, it is found that
The magnitude of the resultant of the addition of two vectors is always less than or equal to the sum of the magnitudes of individual vectors.
That is; $∣ ∣ \to a + b ∣ ∣ \leq | \to a | + ∣ ∣ \to b ∣ ∣$
2. The magnitude of the resultant of the addition of two vectors is always greater than the difference of the magnitudes of individual vectors.
That is; $∣ ∣ \to a + b ∣ ∣ > | \to a | - ∣ ∣ \to b ∣ ∣$
Thus,
Option C) less than or equal to $| \to a | + ∣ ∣ \to b ∣ ∣$ .

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When two vectors, →a and →b are added, the magnitude of the resultant vector is always

When two vectors, $\to a$ and $\to b$ are added, the magnitude of the resultant vector is always