Find the angle between the vectors - and -k-

Let a= î ĵ+0k̂ and b = 0î+ĵ k̂ a.b=(1)(0)+( 1)(1)+0( 1)= 1 | a |=√(1+1)=√(2) nbsp; and nbsp; | b |=√(1+1)=√(2) nbsp; ∴cos θ=a.b/ | a | | b |= 1/√(2).√( ...

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Byju's Answer

Standard XII

Mathematics

Definition of Vector

Find the angl...

Question

Find the angle between the vectors $^i -^j$ and $^j -^k$ .

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Solution

Let $\to a =^i -^j + 0^k$ and $\to b = 0^i +^j -^k$

$\to a . \to b = (1) (0) + (- 1) (1) + 0 (- 1) = - 1$

$∣ ∣ \to a ∣ ∣ = \sqrt{1 + 1} = \sqrt{2}$ and $∣ ∣ ∣ \to b ∣ ∣ ∣ = \sqrt{1 + 1} = \sqrt{2}$

$∴ cos θ = \frac{\to a . \to b}{∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣} = \frac{- 1}{\sqrt{2} . \sqrt{2}} = \frac{- 1}{2} = - cos \frac{π}{3}$

$\Rightarrow cos θ = cos (π - \frac{π}{3})$

$\Rightarrow cos θ = cos \frac{2 π}{3}$

$\Rightarrow θ = \frac{2 π}{3}$
Hence, the angle between the vectors $^i -^j$ and $^j -^k$ is $\frac{2 π}{3}$

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Find the angle between the vectors ^i−^j and ^j−^k.

Find the angle between the vectors $^i -^j$ and $^j -^k$ .