1.

(a) यदि सदिश `vecA = A_(x) hati + A_(y) hatj + A_(z) hatk` तथा सदिश `vecB = B_(x)hati + B_(y) hatj + B_(z) hatk` के बीच का कोण `theta` हो, तो सिद्ध कीजिए कि ` cos theta = (A_(x)B_(x) + A_(y)B_(y) + A_(z)B_(z))/(sqrt(A_(x)^(2) + A_(y)^(2) + A_(z)^(2)) sqrt(B_(x)^(2) + B_(y)^(2) + B_(z)^(2)` (b) सदिश `(hati + hatj)` तथा `(hatj + hatk)` के बीच कोण कितना होगा ?

Answer» ` cos theta = (0+1+0)/(sqrt(1^(2) + 1^(2))sqrt(1^(2) +1^(1))) = (1)/(sqrt(2)sqrt(2)) = (1)/(2)`


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