In the given figure `bar(PQ)` is a line. Ray `bar(OR)` is perpendicular to line `bar(PQ) . bar(OS)` is another ray lying between rays `bar(OP) `and `bar(OR)` . Prove that `angleROS = (1)/(2) angleQOS − anglePOS`

In the given figure oversetharr( PQ) is a line. Ray oversetharr(OR) is perpendicular to line oversetharr (PQ). Oversetharr(OS ) is another ray lying between rays oversetharr(OP) and oversetharr(OR) . Prove that, angleROS = 1/2 ( angleQOS - anglePOS) .

If bar(a) = 2bar(i) + 2bar(j) - 3bar(k), bar(b) = 3bar(i) - bar(j) + 2bar(k) then find the angle between 2bar(a)+bar(b) and bar(a) + 2bar(b) .

If bar(a) = 6bar(i) + 2bar(j) + 3bar(k) and bar(b) = 2bar(i) - 9bar(j) + 6bar(k) , then find bar(a).bar(b) amd the angle between bar(a) and bar(b) .

In the figure, O is the centre of the circle and AB = CD. OM is perpendicular on bar(AB) and bar(ON) is perpendicular on bar(CD) . Then prove that OM = ON.

Find unit vector perpendicular to both bar(i) + bar(j) + bar(k) and 2bar(i) + bar(j) + 3bar(k) .

The resultant of bar(u) and bar(v) is perpendicular to bar(u) and has a magnitude equal to half of the magnitude of bar(v) . The angle between bar(u) " & " bar(v) is

If bar(a) , bar(b) and bar(a)-sqrt2bar(b) are unit vectors, then what is the angle between bar(a), bar(b) ?

In the given figure lines bar(XY) and bar(MN) intersect at O. If ∠POY = 90^(@) and a: b = 2 : 3, find c.

Draw the figures for the following : bar(OP)

Let bar(a) = 2bar(i)-bar(j)+bar(k), bar(b) = 3bar(i) + 4bar(j) -bar(k) and if theta is the angle between bar(a), bar(b) then find sin theta .