" 51."(3)/(4)fa((3)/(5))^(3)((3)/(5))^(-6)=((3)/(5))^(2x-1)vec e uarr,vec ix=?

Take away: (6)/(5)x^(2)-(4)/(5)x^(3)+(5)/(6)+(3)/(2)x om (x^(3))/(3)-(5)/(2)x^(2)+(3)/(5)x+(1)/(4)

Find the angle between the following pairs of lines : (i) vec(r) = 3 hat(i) + 2 hat(j) - 4 hat(k) + lambda (hat(i) + 2 hat(j) + 2 hat(k) ) . vec(r) = 5 hat(j) - 2 hat(k) + mu ( 3 hat(i) + 2 hat(j) + 6 hat(k)) (ii) vec(r) = 3 hat(i) + hat(j) - 2 hat(k) + lambda (hat(i) - hat(j) - 2 hat(k) ) . vec(r) =(2 hat(i) - hat(j) - 56 hat(k)) + mu ( 3 hat(i) - 5 hat(j) - 4 hat(k)) (iii) (x-2)/(2) = (y - 1)/(5) = (z + 3)/(-3) and (x + 2)/(-1) = (y - 4)/(8) = (z - 5)/(4) (iv) (x - 4)/(3) = (y + 1)/(4) = (z - 6)/(5) and (x-5)/(1) = (2y +5)/(-2) = (z - 3)/(1) (v) (5 -x)/(3) = (y + 3)/(-4) , z = 7 and x = (1-y)/(2) = (z - 6)/(2) (vi) (x + 3)/(3) = (y - 1)/(5) = (z + 3)/(4) and (x + 1)/(1) = (y - 4)/(1) = (z-5)/(2) .

Observe the following pattern (1x2)+(2x3)=(2x3x4)/(3)(1x2)+(2x3)+(3x4)=(3x4x5)/(3)(1x2)+(2x3)+(3x4)+(4x5)=(4x5x6)/(3) and find the of (1x2)+(2x3)+(3x4)+(4x5)+(5x6)

If the two adjacent sides of two rectangles are represented by vectors vec p=5 vec a-3 vec b ; vec q=- vec a-2 vec b \ and \ vec r=-4 vec a- vec b ; vec s=- vec a+ vec b , respectively, then the angel between the vector vec x=1/3( vec p+ vec r+ vec s) \ and \ vec y=1/5( vec r+ vec s) is a. -cos^(-1)((19)/(5sqrt(43))) b. cos^(-1)((19)/(5sqrt(43))) c. pi-cos^(-1)((19)/(5sqrt(43))) d. cannot be evaluate

If the two adjacent sides of two rectangles are represented by vectors vec p=5 vec a-3 vec b ; vec q=- vec a-2 vec ba n d vec r=-4 vec a- vec b ; vec s=- vec a+ vec b , respectively, then the angel between the vector vec x=1/3( vec p+ vec r+ vec s)a n d vec y=1/5( vec r+ vec s) is a.cos^(-1)((19)/(5sqrt(43))) b. cos^(-1)((19)/(5sqrt(43))) c. picos^(-1)((19)/(5sqrt(43))) d. cannot be evaluate

For teaching the concept of probability, Mrs. Verma decided to use two dice. Shet took a pair of die and write all the possible outcomes on the blackboard. All possible outcomes wave: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6) (2,1), (2,2), (2,3), (2,4), (2,5), (2,6) (3,1), (3,2), (3,3), (3,4), (3,5), (3,6) (4,1), (4,2), (4,3), (4,4), (4,5), (4,6) (5,1), (5,2), (5,3), (5,4), (5,5), (5,6) (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) The probability that 5 will come up at least once is:

Find the resultant of vec(F_(1)) + vec(F_(2)) - vec(F_(3)) ( sin 37^(@) = (3)/(5) , cos 37^(@) = (4)/(5))

Find a vector of magnitude sqrt(51) and makes equal angle with the vectors vec(a)=(1)/(3)(hati-2hatj+2hatk),vec(b)=(1)/(5)(-4hati-3hatk) and vec( c )=hatj .

In R^(3),vec(x)=(2,3,6),vec(y)=(6, -2,3) and vec(z)=(3,6,-2) , then find 2vec(x)+vec(y)-vec(z) .