若三角形abc的面积是2,cosA=5分之2,则向量AB·向量AC等于多少
问题描述:
若三角形abc的面积是2,cosA=5分之2,则向量AB·向量AC等于多少
答
S = 0.5|AB||AC|sinA=2 => |AB||AC|sinA = 4
cosA = 2/5 => sinA = 根号21/5 => |AB||AC| = 4/(根号21/5) = 20/根号21
=> AB点乘AC =|AB||AC|cosA = 20/根号21 * 2/5 = 8/根号21