If angle between unit vectors `bar(P)` and `bar(Q)` is `60^(0)` then `|bar(P)+bar(Q)|` is

The angle between the unit vectors bar(a) and bar(b) is theta . If bar(a)-sqrt(2)bar(b) is a unit vector then theta = …………

If theta is the angle between unit vectors bar(A) and bar(B) then (1-bar(A).bar(B))/(1+bar(A)*bar(B)) is equal to

Let bar(a), bar(b), bar(c ) be unit vectors, suppose that bar(a). bar(b) = bar(a). bar(c )= 0 and the angle between bar(b) and bar(c ) is pi//6 then show that bar(a)= +-2 (bar(b) xx bar( c))

vec(P), vec(Q), vec(R ), vec(S) are vectors of equal magnitude. If bar(P) + vec(Q) - vec(R )= O angle between vec(P) and vec(Q) " is " theta_(1) . If bar(P) + bar(Q) - bar(S) = O angle between bar(P) and bar(S) " is " theta_(2) . The ratio of bar(theta)_(1) " to " theta_(2) is

bar(a),bar(b) and bar( c ) are unit vectors. bar(a).bar(b)=0=bar(a).bar( c ) and the angle between bar(b) and bar( c ) is (pi)/(3) . Then |bar(a)xx bar(b)-bar(a)xx bar( c )|= …………..

If the vector -bar(i)+bar(j)-bar(k) bisects the angles between the vector bar(c) and the vector 3bar(i)+4bar(j) ,then the unit vector in the direction of bar(c) is

If the vector -bar(i)+bar(j)-bar(k) bisects the angles between the vector bar(c) and the vector 3bar(i)+4bar(j) , then the unit vector in the direction of bar(c) is

Consider two points P and Q with position vectors bar(OP) = 3bar(a) - 2bar(b) and bar(OQ) = bar(a)+bar(b) . Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1 externally.

Consider two points P and Q with position vectors bar(OP) = 3bar(a) - 2bar(b) and bar(OQ) = bar(a)+bar(b) . Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1 (i) internally.