If `(2)/(3)j-(1)/(4)k=(5)/(2)`, what is the value of `8j-3k`?

If 3j-(k_5)=16-4k , what is the value of j+k ?

Whenever j and k are positive integers such that (sqrt3)^(j) = 27^(k) , what is the value of j/k ?

[(1,3),(-2,4)]+[(11,5),(-6,12)]=K[(3,2),(J,M)] . Find the value of K+J+M.

If a=2i-3j+5k, b=3i-4j+5k" and "c=5i-3j-2k then volume of the parallelopiped with coterminus edges a+b, b+c, c+a is _______

If abs(a)^(2)=8" and "a times (i+j+2k)=0 then the value of a*(-i+j+4k) is

If a and b are vectors such that |a+b|=sqrt(29) and a xx(2i+3j+4k)=(2i+3j+4k)xx b, then a possivalue of (a+b)*(-7i+2j+3k) is

If the vectors hat(i)-2hat(j)+hat(k),ahat(i)+5hat(j)-3hat(k)and5hat(i)-9hat(j)+4hat(k) are coplanar, then the value of a is

{:(I."Area of the parallelogram with diagonals" 3i + j - 2k. i - 3j + 4k, a.(sqrt(569))/(4)), (II. "Area of the triangle whose adjacent sides are" 3i + 4j "and" i - 3j + 4k, b. (2)/(sqrt(14))),(III. "Volume of parallelopiped whose edges are" 2i - 3j. i + j - k. 3i - k, c. 5 sqrt(3)),(IV. "Projection of" 2i + 3j - 2k "in the direction of" i + 2j + 3k, d. 4),(, e. 2//3)):}"

A force vec(F) = (4hat(i) - 3hat(j) - 5hat(k)) N moves a body for (3hat(i) + 6hat(j) + 3hat(k)) m to (ahat(i) - 8hat(j) + 5hat(k)) m. If the work done by the force is 8j, the value of .a. is