Vectors A-B and C have magnitudes 5- 5-2 and 5 respectively and direction of A- B and C are towards East- North - East and North respectively- If - and - are unit vectors along East and North respectively- The magnitude and direction of the resultant respectively will be

A = 5 î, C = 5 ĵ B = 5√(2)cos 45 î + 5√(2)sin 45 ĵ =5 î + 5 ĵ A + B + C = 5 î + 5 î + 5 ĵ + 5ĵ = 10 î + 10ĵ |A+ B+C| = √((10)^2 +(10)^2) = 10 √(2) tanθ = 1010 = ...

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Byju's Answer

Standard XII

Physics

Vector Addition

Vectors A,B a...

Question

Vectors $\to A, \to B$ and $\to C$ have magnitudes $5, 5 \sqrt{2}$ and 5 respectively and direction of $\to A, \to B$ and $\to C$ are towards East, North - East and North respectively. If $^i$ and $^j$ are unit vectors along East and North respectively. The magnitude and direction of the resultant respectively will be

10 \sqrt{2}

towards north-east

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10

and

45^{o}

from north-east

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10

and

45^{o}

from north

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10 \sqrt{2}

and

45^{o}

from north-west

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Solution

The correct option is A $10 \sqrt{2}$ towards north-east
$\to A = 5^i, \to C = 5^j$
$\to B = 5 \sqrt{2} cos 45^i + 5 \sqrt{2} sin 45^j$
$= 5^i + 5^j$
$\to A + \to B + \to C = 5^i + 5^i + 5^j + 5^j = 10^i + 10^j$
$| \to A + \to B + \to C | = \sqrt{(10)^{2} + (10)^{2}} = 10 \sqrt{2}$
$tan θ = \frac{10}{10} = 1$
$θ = 45^{\circ}$
Hence direction is North-East.

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Vectors →A,→B and →C have magnitudes 5,5√2 and 5 respectively and direction of →A,→B and →C are towards East, North - East and North respectively. If ^i and ^j are unit vectors along East and North respectively. The magnitude and direction of the resultant respectively will be

The correct option is A 10√2 towards north-east →A=5^i,→C=5^j →B=5√2cos45^i+5√2sin45^j =5^i+5^j →A+→B+→C=5^i+5^i+5^j+5^j=10^i+10^j |→A+→B+→C|=√(10)2+(10)2=10√2 tanθ=1010=1 θ=45∘ Hence direction is North-East.