Given:
#color(red)(vec a=6i + 5j + 7k#
#color(red)(vec b=3i - 4j + 8k#
#color(green)(cos theta = (vec a*vec b)/(|a|*|b|)#
#rArr [(6*3)+(5)*(-4) + (7)(8)]/[sqrt(6^2+5^2+7^2)*sqrt(3^2+(-4)^2+8^2]#
#rArr [18-20 + 56]/[sqrt(36+25+49)*sqrt(9+16+64]#
#rArr 54/(sqrt(110)*sqrt(89))#
#rArr (54)/[(10.48809)*(9.433981)]~~ (54/98.94443)#
Hence,
#color(green)(cos theta ~~ (0.545760895)#
To find the required angle, we must find the value of #color(green)(theta#.
#theta=cos^-1(0.545760895)#
Hence,
#theta ~~ 56.92332412#
The angle between the vectors #color(green)(<6 , 5 , 7 > and < 3 , -4 , 8 > # is given by #color(blue)(56.92^@# approx.
Hope it helps.
