Related InterviewSolutions

• When does `|vec(a)+vec(b)|=|vec(a)|+|vec(b)|` hold?
• What is the angle which the vector `(hat(i)+hat(j)+sqrt(2)hat(k))` makes with the z-axis ?A. `(pi)/(4)`B. `(pi)/(3)`C. `(pi)/(6)`D. `(2pi)/(3)`
• If `vec(a)` and `vec(b)` are vectors such that `|vec(a)|=sqrt(3), |vec(b)|=2` and `vec(a).vec(b)=sqrt(6)` then the angle between `vec(a) and vec(b)` isA. `(pi)/(6)`B. `(pi)/(3)`C. `(pi)/(4)`D. `(2pi)/(3)`
• Find the direction cosines of a vector which is equally inclined to the x-axis, y-axis and z-axis.
• Find the direction cosines of the vector ` hat i+2 hat j+3 hat k`.
• If ` vec a=x hat i+2 hat j- z hat k`and ` vec b=3 hat i- y hat j+ hat k`are two equal vectors, thenwrite the value of `x+y+zdot`
• If `vec(a)` and `vec(B)` are two vectors such that `|vec(a)|=|vec(b)|=sqrt(2)` and `vec(a).vec(b)=-1`, find the angle between `vec(a)` and `vec(b)`.A. `(pi)/(6)`B. `(pi)/(4)`C. `(pi)/(3)`D. `(2pi)/(3)`
• If `vec(a)=(hat(i)+2hat(j)-3hat(k)) and vec(b)=(3hat(i)-hat(j)+2hat(k))` then the angle between `(vec(a)+vec(b))` and `(vec(a)-vec(b))` isA. `(pi)/(3)`B. `(pi)/(4)`C. `(pi)/(2)`D. `(2pi)/(3)`
• If `hat(a) and hat(b)` are unit vectors such that `(hat(a) + hat(b))` is a unit vector, what is the angle between `hat(a) and hat(b)`?
• Write the direction cosines of the vector `-2 hat i+ hat j-5 hat k`A. `-2, 1, -5`B. `(1)/(3),(-1)/(6),(-5)/(6)`C. `(2)/(sqrt(30)), (1)/(sqrt(30)),(5)/(sqrt(30))`D. `(-2)/(sqrt(30)),(1)/(sqrt(30)),(-5)/(sqrt(30))`