Represent graphically the displacement of (i) 30 km 60° west of north (ii) 60 km 50° south of east.

Represent graphically the displacement of 45cm 30°north of east.

Prove that the relation R defined on the set V of all vectors by ‘ \(\overrightarrow{a}\ R\ \overrightarrow{b} \ if \ \overrightarrow{a}=\overrightarrow{b}\) is an equivalence relation on V.

If G is the centroid of a triangle ABC, prove that \(\overrightarrow{GA}\) + \(\overrightarrow{GB}\)  + \(\overrightarrow{GC}\) = \(\overrightarrow{0}\).

Find a unit vector along the direction of the vector 5\(\hat{i}\) - 3\(\hat{j}\) + 4\(\hat{k}\) .

Find the direction cosines of a vector whose direction ratios are 2, 3, - 6.

Find the direction cosines of \(\overrightarrow{AB},\) where A is (2, 3, 1) and B is (3, - 1, 2).

Verify whether the following ratios are direction cosines of some vector or not \({1\over 5},{3\over 5},{4\over 5}\)

Find the direction cosines of a vector whose direction ratios are 1, 2, 3