Show that the vector i^+j^+k^is equally inclined to the axes OX, OY and OZ.

Solution: a=pi^+qj^+rk^cosα=p2+q2+r2pcosβ=p2+q2+r2qcosγ=p2+q2+r2rcosα=1+1+11=31similarly,cosβ=31andcosγ=31cosα=cosβ=cosγ

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Show that the vector {{i}}+{{j}}+{{k}}is equally inclined to t

Question

Show that the vector $\hat{i} + \hat{j} + \hat{k}$ is equally inclined to the axes OX, OY and OZ.

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Amelia Discussed

Show that the vector

\hat{i} + \hat{j} + \hat{k}

is equally inclined to the axes OX, OY and OZ.

12 mins ago

Discuss this question LIVE

12 mins ago

Solution:

a = p \hat{i} + q \hat{j} + r \hat{k}

cos α = \frac{p}{p ^{2} + q ^{2} + r ^{2}}

cos β = \frac{q}{p ^{2} + q ^{2} + r ^{2}}

cos γ = \frac{r}{p ^{2} + q ^{2} + r ^{2}}

cos α = \frac{1}{1 + 1 + 1} = \frac{1}{3}

similarly,

cos β = \frac{1}{3} and cos γ = \frac{1}{3}

cos α = cos β = cos γ

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Question Text	Show that the vector $\hat{i} + \hat{j} + \hat{k}$ is equally inclined to the axes OX, OY and OZ.
Answer Type	Text solution:1
Upvotes	150