If -a-b-60-a-b-40- and -b-46 - Find -a-

The correct option is B 22Here, |a + b| =60 Squaring both the sides, nbsp; |a + b|^2 =(60)^2 nbsp; |a|^2+|b|^2 + 2a . b = 3600 nbsp; nbsp; nbsp; nb ...

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Byju's Answer

Standard XII

Physics

Vector Addition

If |a⃗+b⃗|=60...

Question

If $| \to a + \to b | = 60, | \to a - \to b | = 40,$ and $| \to b | = 46$ . Find $| \to a |$

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Solution

The correct option is B 22
Here, $| \to a + \to b | = 60$
Squaring both the sides,
$| \to a + \to b |^{2} = (60)^{2}$
$| \to a |^{2} + | \to b |^{2} + 2 \to a . \to b = 3600$ ...(i)
Now, $| \to a - \to b | = 40$
Squaring both the sides,
$| \to a - \to b |^{2} = (40)^{2}$
$| \to a |^{2} + | \to b |^{2} - 2 \to a . \to b = 1600$ ...(ii)

Adding (i) and (ii)
$2 | \to a |^{2} + 2 | \to b |^{2} + 2 \to a . \to b - 2 \to a . \to b = 3600 + 1600$
$2 | \to a |^{2} + 2 \times 46^{2} = 5200$
$2 | \to a | = 5200 - 4232$
$2 | \to a |^{2} = 968$
$| \to a |^{2} = \frac{968}{2}$
$| \to a |^{2} = 484$
$| \to a | = \sqrt{484}$
$| \to a | = 22$

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Similar questions

Q. If

∣ ∣ \to a + \to b ∣ ∣ = 60, ∣ ∣ \to a - \to b ∣ ∣ = 40

and

| \to a | = 22

then find

∣ ∣ \to b ∣ ∣ .

Q. If for vectors

\to a

and

\to b

| \to a | = 4, ∣ ∣ \to b ∣ ∣ = 3

and

\to a \to b = 8

, then find

∣ ∣ \to a \times \to b ∣ ∣

Q. Find

| \to a |

and

| \to b |

, if

(\to a + \to b) . (\to a - \to b) = 8

and

| \to a | = 8 | \to b |

Q. If

| \to a | = 2, | \to b = 5 |

and

| \to a \times | \to b | = 8

find the

\to a, \to b

Q. I : If

| \to a + \to b | = | \to a - \to b |

, then

(\to a, \to b) = \frac{π}{2}

.
II : If

\to a, \to b, \to a + \to b

are unit vectors, then

(\to a, \to b) = \frac{2 π}{3}

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If |→a+→b|=60,|→a−→b|=40, and |→b|=46. Find |→a|

If $| \to a + \to b | = 60, | \to a - \to b | = 40,$ and $| \to b | = 46$ . Find $| \to a |$