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Standard XII

Mathematics

Addition of Vectors

The vectors b...

Question

The vectors b and c are in the direction of north-east and north-west respectively and $| b | = | c | = 4$ . The magnitude and direction of the vector d = c - b, are

\sqrt{2}

, towards north

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\sqrt{2}

, towards west

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4, towards east

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4, towards south

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Solution

The correct option is B 4 $\sqrt{2}$ , towards west
Clearly, $b ⊥ c, ∴ b . c = 0$
Now, d = c - d $\Rightarrow | d |^{2} = | c - b |^{2}$
$= | c |^{2} + | b |^{2} - 2 b . c = 16 + 16 - 0$
$\Rightarrow | d | = \sqrt{32} = 4 \sqrt{2}$ and direction of d is west.

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The vectors b and c are in the direction of north-east and north-west respectively and |b|=|c|=4. The magnitude and direction of the vector d = c - b, are

The correct option is B 4√2, towards westClearly, b⊥c,∴b.c=0 Now, d = c - d ⇒|d|2=|c−b|2 =|c|2+|b|2−2b.c=16+16−0 ⇒|d|=√32=4√2 and direction of d is west.

The vectors b and c are in the direction of north-east and north-west respectively and $| b | = | c | = 4$ . The magnitude and direction of the vector d = c - b, are

The correct option is B 4 $\sqrt{2}$ , towards west
Clearly, $b ⊥ c, ∴ b . c = 0$
Now, d = c - d $\Rightarrow | d |^{2} = | c - b |^{2}$
$= | c |^{2} + | b |^{2} - 2 b . c = 16 + 16 - 0$
$\Rightarrow | d | = \sqrt{32} = 4 \sqrt{2}$ and direction of d is west.