Find the scalr and vector products of two vectors ` vec a =(3 hat I - 4 hat j + 5 hat k) and

Find the scalar and vector products of two vectors vec(a)=(2hat(i)-3hat(j)+4hat(k)) and vec(b)(hat(i)-2hat(j)+3hat(k)) .

Find the scalar and vector paroducts of two vectors. a=(3hat(i)-4hat(j)+5hat(k)) " and " b=(-2hat (i) +hat(j)-3hat(k))

Find a unit vector parallel to the resultant of vectors vec A = 3 hat I + 3 hat j - 2 hat k and vec B= hat i- 5 hat j + hat k .

Find the sine of the angle between the vectors vec A = 3 hat i - 4 hat j + 5 hat k and vec B = hat i - hat j + hat k .

Which of the following vector is perpendicular to the vector vec A = 2 hat i + 3 hat j + 4 hat k ?

A vector vec C when added to the resultant of the vectors vec A = 3 hati -4 hat j + 5 hat k and vec B = 2 vec 2 hat I + 3 hat j -4 hat k giv es a unit vector along y-axis. Find the magnitude of vec C .

Find a unit vector perpendicular to each one of the vectors vec(a) = 4 hat(i) - hat (j) + 3hat(k) and vec(b) = 3 hat(i) + 2 hat(j) - hat(k) .

Find the area of the rriangle formed by the tips of the vectors, vec a= (2 hat I - hat j+ 3 hat k), vec b= 4 hat I + 3 hat j-hat k , vec C= 3 hat I - hat j + 2 hat k .

Find the sine of the angle between the vectors vec(a) =(2 hat(i) - hat(j) + 3 hat(k)) and vec(b) = (hat(i) + 3 hat(j) + 2 hat(k)).

The scalar product of the vector vec a=hat i+hat j+hat k with a unit vector along the sum of the vectors vec b=2hat i+4hat j-5hat k and vec c=lambdahat i+2hat j+3hat k is equal to 1. Find the value of lambda and hence find the unit vector along vec b+vec r