Let ` vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot]` denotes the greatest integer function. Then the vectors ` vecf(5/4)a n df(t),0lttlti` are(a) parallel to each other(b) perpendicular(c) inclined at `cos^(-1)2 (sqrt(7(1-t^2)))` (d)inclined at `cos^(-1)((8+t)/sqrt (1+t^2))`;

Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] denotes the greatest integer function. Then the vectors vecf(5/4)a n df(t),0lttlt1 are(a) parallel to each other(b) perpendicular(c) inclined at cos^(-1)2 (sqrt(7(1-t^2))) (d)inclined at cos^(-1)((8+t)/(9sqrt (1+t^2))) ;

Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] denotes the greatest integer function. Then the vectors vecf(5/4)a n df(t),0lttlt1 are(a) parallel to each other(b) perpendicular(c) inclined at cos^(-1)2 (sqrt(7(1-t^2))) (d)inclined at cos^(-1)((8+t)/(9sqrt (1+t^2))) ;

Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] denotes the greatest integer function. Then the vectors vecf(5/4) and vecf(t) , 0 < t < 1 are (a) parallel to each other (b) perpendicular to each other (c) inclined at cos^(-1)(2/(sqrt(7(1-t^2)))) (d) inclined at cos^(-1)((8+t)/(9*sqrt(1+t^2)))

let vec f(t)=[t]hat i-(t-[t])hat j+[t+1]hat k be a vector.where [.] is a greatest integer function if f((5)/(4)) and hat i+lambdahat j+muhat k are parallel vectors then (lambda,mu)

Differentiate cos^-1(1/(sqrt(1+t^2))) w.r.t sin^-1(t/(sqrt(1+t^2)))

Derivative of cos^(-1)[(1)/(sqrt(t^(2)+1)]w.r.tsin^(-1)[t/(sqrt(t^(2)+1))] is

If Vectors vec(A)= cos omega t(i)+ sin omega t(j) and vec(B)=cosomegat/(2)hat(i)+sinomegat/(2)hat(j) are functions of time. Then the value of t at which they are orthogonal to each other is

If Vectors vec(A)= cos omega t hat(i)+ sin omega t hat(j) and vec(B)=(cos)(omegat)/(2)hat(i)+(sin)(omegat)/(2)hat(j) are functions of time. Then the value of t at which they are orthogonal to each other is