A vector ( v =4 i -3 j +2 k ) is considered

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

A vector v=4i^−3j^+2k^\mathbf{v}=4\hat{i}-3\hat{j}+2\hat{k} is considered. (i) State the rule for obtaining the product of a scalar and a vector. (ii) Explain, without actual calculation, how the direction and magnitude of −12 v-\dfrac{1}{2}\,\mathbf{v} compare with those of v.\mathbf{v}. (iii) Obtain the component form of −12 v.-\dfrac{1}{2}\,\mathbf{v}. (iv) Calculate the magnitudes of v\mathbf{v} and −12 v-\dfrac{1}{2}\,\mathbf{v} and verify that the numerical ratio of their magnitudes equals the absolute value of the scalar used.

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