Find the scalar product of the vectors \vec{a}=6\hat{i}-7\hat{j}+5\hat{k} \,and \,\vec{b}=6\hat{i}-7\hat{k}

(a) 1

(b) 8

(c) 6

(d) 3

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My question is taken from Product of Two Vectors-1 topic in division Vector Algebra of Mathematics – Class 12

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The correct answer is (a) 1

The explanation is: If \vec{a} \,and \,\vec{b} are two vectors, where a_1, a_2, a_3 are the components of vector \vec{a} \,and \,b_1, b_2, b_3 are the components of vector \vec{b}, then the scalar product is given by

\vec{a}.\vec{b}=a_1 b_1+a_1 b_2+a_3 b_3

(6\hat{i}-7\hat{j}+5\hat{k}).(6\hat{i}-7\hat{k})=6(6)-7(0)+5(-7)=36-35=1.