+91-8076753736[email protected]
logo
logo
-->

Vector Algebra

Question
CBSEENMA12034016
Wired Faculty App

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 1 over denominator square root of 3 end fraction.

Solution

Let straight a with rightwards arrow on top space equals space straight a subscript 1 straight i with hat on top space plus space straight a subscript 2 straight j with hat on top space plus space straight a subscript 3 straight k with hat on top be the vector, where straight a subscript 1 comma space straight a subscript 2 comma space straight a subscript 3 are the direction ratios of the vector.
           Since vector is equally inclined to the axes
     therefore space space space space straight a subscript 1 space equals space straight a subscript 2 space equals space straight a subscript 3 space equals space straight p comma space space say. therefore space space space straight a with rightwards arrow on top space equals space straight p space straight i with hat on top space plus space straight p space straight j with hat on top space plus straight p space straight k with hat on top therefore space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of straight p squared plus straight p squared plus straight p squared end root space equals space square root of 3 space straight p squared end root space equals space square root of 3 space straight p therefore space space space space space space space space space space space space space straight a with hat on top space equals space fraction numerator straight a with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction space equals space fraction numerator straight p over denominator square root of 3 space straight p end fraction straight i with hat on top space plus space fraction numerator straight p over denominator square root of 3 space straight p end fraction straight j with hat on top space plus space fraction numerator straight p over denominator square root of 3 space straight p end fraction straight k with hat on top space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 1 over denominator square root of 3 end fraction straight i with hat on top space plus space fraction numerator 1 over denominator square root of 3 end fraction straight j with hat on top space plus space fraction numerator 1 over denominator square root of 3 end fraction straight k with hat on top
therefore   direction cosines of a vector equally inclined to axes are fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 1 over denominator square root of 3 end fraction.

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
40 watt

Classify the following measures as scalars and vectors.
10–19 coulomb

Classify the following measures as scalars and vectors.
20 m/s2

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Classify the following measures as scalars and vectors.
velocity

Classify the following measures as scalars and vectors.
work done

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation