If the resultant of three forces `vec(F_(1))=phat(i)+3hat(j)-hat(k), vec(F_(2))=6hat(i)-hat(k) " and " vec(F_(3))=-5hat(i)+hat(j)+2hat(k)` acting on a particle has a magnitude equal to 5 units, then the value of p is -

If the resultant of three forces vec F_1=p hat i+3 hat j- hat k , vec F_2=6 hat i- hat k and vec F_3=-5 hat i+ hat j+2 hat k acting on a parricle has magnitude equal to 5 units, then the value of p is a. -6 b. -4 c. 2 d. 4

The lines vec(r)=hat(i)+hat(j)-hat(k)+lamda(3hat(i)-hat(j)) and vec(r)=(4hat(i)-hat(k))+mu(2hat(i)+3hat(k)) -

Find the value of lamda if three vectors vec(a) = 2hat(i) - hat(j) + hat(k), vec(b) = hat(i) + 2hat(j) - 3hat(k) and vec(c) = 3hat(i) + lamda hat(j) + 5hat(k) are coplanar

If vec(a)=2hat(i)+hat(j)-3hat(k), vec(b)=5hat(i)+4hat(j)+2hat(k) " and " vec(c)=3hat(i)-3hat(j)-2hat(k) , then find the magnitude of the vector vec(a)+vec(b)+2vec(c) and a unit vector in the direction of this vector.

If vec(a)=2hat(i)-2hat(j)+hat(k), vec(b)=2hat(i)+3hat(j)+6hat(k) " and " vec(c)=-hat(i)+2hat(k) , then find the magnitude and direction of the vector vec(a)-vec(b)+2vec(c) .

If vec(a)=hat(i)+hat(j)+hat(k), vec(b)=2hat(i)-hat(j)+3hat(k) " and " vec(c)=hat(i)-2hat(j)+hat(k) find a unit vector in a direction parallel to vector (2vec(a)-vec(b)+3vec(c)) .

Find the angle between the lines vec(r)=(3hat(i)+hat(j)-4hat(k))+t(hat(i)+hat(j)+hat(k)) and vec(r)=(5hat(i)-hat(j))+t'(3hat(i)+2hat(j)+4hat(k))

The lines vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k)) and vec(r)=hat(i)+s(-10hat(i)-4hat(j)-2hat(k)) are -

If vec(OA)=hat(i)-2hat(k) " and " vec(OB)=3hat(i)-2hat(j) then the direction cosines of the vector vec(AB) are -

If vectors vec(alpha)=2hat(i)+3hat(j)-6hat(k) " and " vec(beta)=phat(i)-hat(j)+2hat(k) are parallel, then the value of p is -