Vector A of magnitude 4 units is directed along the positive x-axis- Another vector B of magnitude 3 units lies in the x-y plane and makes an angle 30- with the positive x-axis as shown in the figure- Then A-B is

Let î and ĵ be the unit vectors along positive x and y axes respectively. Then A=4î B=3 cos 30^∘î+3 sin 30^∘ĵ =3√(3)/2î+3/2ĵ A.B=4î.(3√(3)/2î+3/2ĵ)=6√(3)(∵î.î=1 ...

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Byju's Answer

Standard XII

Physics

Vector Component

Vector A of m...

Question

Vector $\to A$ of magnitude 4 units is directed along the positive x-axis. Another vector $\to B$ of magnitude 3 units lies in the x-y plane and makes an angle $30^{\circ}$ with the positive x-axis as shown in the figure. Then $\to A . \to B$ is

6 units

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$6 \sqrt{2}$ units

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$6 \sqrt{3}$ units

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12 units

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Solution

The correct option is C
$6 \sqrt{3}$ units

Let $^i$ and $^j$ be the unit vectors along positive x and y axes respectively. Then
$\to A = 4^i$
$\to B = 3 c o s 30^{\circ}^i + 3 s i n 30^{\circ}^j$
$= \frac{3 \sqrt{3}}{2}^i + \frac{3}{2}^j$
$\to A . \to B = 4^i . (\frac{3 \sqrt{3}}{2}^i + \frac{3}{2}^j) = 6 \sqrt{3}$ $(∵^i .^i = 1;^i .^j = 0)$ .
Hence, the correct option is (c).

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Vector $\to A$ of magnitude 4 units is directed along the positive x-axis. Another vector $\to B$ of magnitude 3 units lies in the x-y plane and makes an angle $30^{\circ}$ with the positive x-axis as shown in the figure. Then $\to A . \to B$ is

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Vector →A of magnitude 4 units is directed along the positive x-axis. Another vector →B of magnitude 3 units lies in the x-y plane and makes an angle 30∘ with the positive x-axis as shown in the figure. Then →A.→B is

The correct option is C 6√3 units Let ^i and ^j be the unit vectors along positive x and y axes respectively. Then →A=4^i →B=3 cos 30∘^i+3 sin 30∘^j =3√32^i+32^j →A.→B=4^i.(3√32^i+32^j)=6√3 (∵^i.^i=1;^i.^j=0). Hence, the correct option is (c).

Vector $\to A$ of magnitude 4 units is directed along the positive x-axis. Another vector $\to B$ of magnitude 3 units lies in the x-y plane and makes an angle $30^{\circ}$ with the positive x-axis as shown in the figure. Then $\to A . \to B$ is