If `bar(a)=phat i+3hat j-7hat k, bar(b)=phat i-phat j+4hat k` and if the angle between `bar(a)` and `bar(b)` is acute, then the values of p lies in.

If bar(P)=hat i+hat j+hat k,bar(Q)=2hat i-hat j-hat k , then bar(P)-bar(Q) is

If bar(a)=2hat i+2hat j+hat k and bar(b)=hat i-hat j-chat k .If angle between bar(a) and bar(b) is 37^(0) .The value of c is (take, cos37^(0)=(4)/(5)

If bar(a)=3hat i-3hat j-4hat k, bar(b)=hat i+2hat j+hat k and bar(c)=3hat i-hat j-2hat k , then [bar(a) bar(b) bar(c)] =

If bar(A)=2hat i+3hat j+6hat k and bar(B)=3hat i-6hat j+2hat k ,then a vector perpendicular to both bar(A) and bar(B) has magnitude K times that of (6hat i+2hat j-3hat k) .Then K is equal to

If bar(a)=hat i+2hat j-hat k and bar(b)=3hat i+hat j-5hat k find a unit vector in a direction parallel to vector (bar(a)-bar(b))

Given two vectors bar(A)=hat i-2hat j-3hat k and bar(B)=4hat i-2hat j+6hat k .The angle made by (bar(A)+bar(B)) with the X -axis is

Let bar(a)=4hat i+3hat j-hat k,bar(b)=5hat i+2hat j+2hat k,bar(c)=2hat i-2hat j)-3hat k and bar(d)=4hat i-4hat j+3hat k; prove that bar(b)-bar(a) and bar(d)-bar(c) are parallel and find the ratio of their moduli.

If bar(a) = 4 hat(i) + 3 hat(k) and bar(b) = - 2 hat(i) + hat(j) + 5 hat(k) then find 2 bar(a) + 5 bar(b)

Given two vectors , bar(A)=hat i-2hat j-3hat k and bar(B)=4hat i-2hat j+6hat k .The angle made by (bar(A)+bar(B)) with the x -axis is

Let bar(a)=3hat i+2hat j+2hat k,bar(b)=hat i+2hat j-2hat k Then a unit vector perpendicular to both bar(a)-bar(b) and bar(a)+bar(b) is