product is defined as the product of magnitudes of two vectors and the COSINE of the angle between the vectors.unit vector u,v,w along U,V,W is :u = U/|U| =  (2i + 3j -6K)/7v = V/|V| =  (6i + 2j + 3k)/7w = W/|W| = ( 3i - 6j - 2k)/7Also if a = x1i +y1j + z1k            and b = x2i + y2j+ z2k,            then a.b = x1.x2 + y1.y2 + z1.z2The scalar product of two vectors a and b, is also known as dot product of a and a unit vector, b is the projection/shadow of vector a on a unit vector b.For eg: If two vectors are perpendicular to each other, and we keep a light from top of vector a.  Then no shadow will FALL on b. That is its projection is zero. ie. a.b = 0 , if a and b is perpendicular.Keeping this in MIND,We need to show that U,V,W are mutually perpendicular,U = 2i + 3j -6k, V = 6i + 2j + 3k, W = 3i - 6j - 2kU.V = 2x6 + 3x2 + -6x3 = 12+6-18=0V.W = 6x3 + 2x-6 +3x-2 = 18-12-6 = 0W.X = 3x2 -6x3 -2x-6 = 6 -18 +12 = 0This implies U,V,W are mutually perpendicular.|U| = unit vector u,v,w along U,V,W is :u = U/|U| =  (2i + 3j -6k)/7v = V/|V| =  (6i + 2j + 3k)/7w = W/|W| = ( 3i - 6j - 2k)/7