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

Let a = i + j + k Direction-cosines of a are i.e., Hence the given vector is equally inclined to the axes OX,OY and OZ .

Vector Algebra — Class 12 Maths Solution

ncert exercise SA NCERT,Page 440,Ex.10.2,Q.No 14

Question

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

Step-by-step Solution

Let $\vec a = \hat i + \hat j + \hat k$
$\therefore$

Direction-cosines of $\vec a$ are
$< \cfrac{1}{{\sqrt {1 + 1 + 1} }}$ , $\cfrac{1}{{\sqrt {1 + 1 + 1} }},\cfrac{1}{{\sqrt {1 + 1 + 1} }} >$

i.e., $< \cfrac{1}{{\sqrt 3 }},\cfrac{1}{{\sqrt 3 }},\cfrac{1}{{\sqrt 3 }} >$

Hence the given vector is equally inclined to the axes $OX,OY$ and $OZ$.

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Vector Algebra. Curated by Sachin Sharma. Free for all students.