Given A -2 -3 - and B - The component of vector A along vector B isA- 1-2-jB- 3-2-jC- 5-2-jD- 7-2-j

The correct option is C Component of A̅ along B̅ = A̅.B̅/|B| = (2î+3ĵ).(î + ĵ)/√(1^2 + 1^2) = 2i . î + 2i . j+3j . î+3ĵ.ĵ/√(1^2+1^2) = 2 + 0 + 0 + 3/√(2) = 5 ...

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Byju's Answer

Standard XII

Physics

Unit Vectors

Given A =2 î+...

Question

Given $A = 2 ˆ i + 3 ˆ j$ and $B = ˆ i + ˆ j$ . The component of vector A along vector B is

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Solution

The correct option is C
Component of $¯ A$ along $¯ B$ = $\frac{¯ A . ¯ B}{| B |} = \frac{(2^i + 3^j) . (^i +^j)}{\sqrt{1^{2} + 1^{2}}}$
$= \frac{2 ˆ i .^i + 2 ˆ i . ˆ j + 3 ˆ j .^i + 3^j .^j}{\sqrt{1^{2} + 1^{2}}}$
$= \frac{2 + 0 + 0 + 3}{\sqrt{2}} = \frac{5}{\sqrt{2}} .$

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Given A=2ˆi+3ˆj and B=ˆi+ˆj. The component of vector A along vector B is

The correct option is C Component of ¯A along ¯B = ¯A.¯B|B|=(2^i+3^j).(^i+^j)√12+12 =2ˆi . ^i+2ˆi . ˆj+3ˆj . ^i+3^j.^j√12+12 =2+0+0+3√2=5√2.

Given $A = 2 ˆ i + 3 ˆ j$ and $B = ˆ i + ˆ j$ . The component of vector A along vector B is

The correct option is C
Component of $¯ A$ along $¯ B$ = $\frac{¯ A . ¯ B}{| B |} = \frac{(2^i + 3^j) . (^i +^j)}{\sqrt{1^{2} + 1^{2}}}$
$= \frac{2 ˆ i .^i + 2 ˆ i . ˆ j + 3 ˆ j .^i + 3^j .^j}{\sqrt{1^{2} + 1^{2}}}$
$= \frac{2 + 0 + 0 + 3}{\sqrt{2}} = \frac{5}{\sqrt{2}} .$