Find the projection of the vector - on the vector -

Let a = î ĵ, b=î+ĵ Projection of a on b is given by, a.b/|b|=(î ĵ).(î+ĵ)/√(1^2+1^2) = 1 × 1+( 1) × 1/√(2)=0 Hence, the projection of vector a on b is 0. ...

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Byju's Answer

Standard XII

Mathematics

Properties of Conjugate of a Complex Number

Find the proj...

Question

Find the projection of the vector $^i -^j$ on the vector $^i +^j$

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Solution

Let $a =^i -^j, b =^i +^j$
Projection of a on b is given by, $\frac{a . b}{| b |} = \frac{(^i -^j) . (^i +^j)}{\sqrt{1^{2} + 1^{2}}} = \frac{1 \times 1 + (- 1) \times 1}{\sqrt{2}} = 0$
Hence, the projection of vector a on b is 0.

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Find the projection of the vector ^i−^j on the vector ^i+^j

Let a=^i−^j, b=^i+^j Projection of a on b is given by, a.b|b|=(^i−^j).(^i+^j)√12+12=1×1+(−1)×1√2=0 Hence, the projection of vector a on b is 0.

Find the projection of the vector $^i -^j$ on the vector $^i +^j$

Let $a =^i -^j, b =^i +^j$
Projection of a on b is given by, $\frac{a . b}{| b |} = \frac{(^i -^j) . (^i +^j)}{\sqrt{1^{2} + 1^{2}}} = \frac{1 \times 1 + (- 1) \times 1}{\sqrt{2}} = 0$
Hence, the projection of vector a on b is 0.