Two vectors are given in Cartesian form: A =4

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

Problem

Two vectors are given in Cartesian form: A=4 i^−2 j^+1 k^,B=−1 i^+3 j^+5 k^.\mathbf{A}=4\,\hat{i}-2\,\hat{j}+1\,\hat{k},\qquad \mathbf{B}=-1\,\hat{i}+3\,\hat{j}+5\,\hat{k}. (i) Calculate the resultant vector R=A+B\mathbf{R}=\mathbf{A}+\mathbf{B}. (ii) Determine the unit vector r^\hat{r} directed along R\mathbf{R}. (iii) Find the angles α, β, γ\alpha,\,\beta,\,\gamma that R\mathbf{R} makes with the positive x−,y−,zx-,y-,z–axes, respectively, correct to two decimal places.

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