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VECTOR CALCULUS, 2.13, 2.2 DIVERGENCE AND CURL-IRROTATIONAL AND, SOLENOIDAL VECTOR FIELDS, • 2.2 (1) DIVERGENCE AND CURL, ở F2, F3, Note :, 2.2.1, Div F, V, F, a z, Note :, 2.2.2 V. F is a scalar quantity, Note :, Curl F, 2.2.3., +k %, X! d XA =, 0 z, Note :, 2.2.4., Curl F is a vector point function., Note :, If F = F,i+ F2j+ F3k then, 2.2.5., k, %3D, ду, F3, F1, F2, 0 z, III. PROBLEMS BASED ON DIVERGENCE AND CURL, ->, Example 2.2.1. If F = xi+yj+?k, then find V., F, and V x F., Solution : Given F = 2i+yj+2R, V. F, ) + (2), 7-7, ax, (A x 7), 2x + 2y + 2z, 2 (x + y + z), %3D, V bait LL iqmara, k, a z, (2?)., = i, ду, +k, ax, a z, = 0i+0j+0k =, Example 2.2.2. If F =, (x -y + 2xz) i + (xz – xy + yz) j+ (z + x) k, find V.F,, ->, ->, V (V . F), V x F, V. (V x F) and V x (V × F) at the point (1, 1, 1)., ->, Solution : Given F, (x? – y + 2xz) i + (xz – xy + yz)j + (z² +x²) k, v.F - - + 2) + z - ay + ye) + +), (xz – xy + yz) +, ду, (2? +x), (2r + 22) + (-x + z) + 2z, = x + 5z, Scanned by CamScanner