Example 27 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra

Last updated at July 14, 2026 by

Example 27 (Supplementary NCERT) - Show that a = i - 2j + 3k, b = -2i

Example 27 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 27 (Supplementary NCERT) Show that the vectors š‘Ž āƒ— = š‘– Ģ‚ āˆ’ 2š‘— Ģ‚ + 3š‘˜ Ģ‚, š‘ āƒ— = āˆ’2š‘– Ģ‚ + 3š‘— Ģ‚ āˆ’ 4š‘˜ Ģ‚ and š‘ āƒ— = š‘– Ģ‚ āˆ’ 3š‘— Ģ‚ + 5š‘˜ Ģ‚ are coplanarThree vectors š‘Ž āƒ—, š‘ āƒ—, š‘ āƒ— are coplanar if [š’‚ āƒ—" " š’ƒ āƒ—" " š’„ āƒ— ] = 0 Given, š’‚ āƒ— = š‘– Ģ‚ āˆ’ 2š‘— Ģ‚ + 3š‘˜ Ģ‚ š’ƒ āƒ— = āˆ’2š‘– Ģ‚ + 3š‘— Ģ‚ āˆ’ 4š‘˜ Ģ‚ š’„ āƒ— = š‘– Ģ‚ āˆ’ 3š‘— Ģ‚ + Ī»š‘˜ Ģ‚ [š’‚ āƒ—" " š’ƒ āƒ—" " š’„ āƒ— ] = |ā– 8(1&āˆ’2&3@āˆ’2&3&āˆ’4@1&āˆ’3&5)| = 1[(3Ɨ5)āˆ’(āˆ’3Ɨāˆ’4) ] āˆ’ (āˆ’2) [(āˆ’2Ɨ5)āˆ’(1Ɨāˆ’4) ] + 3[(āˆ’2Ɨāˆ’3)āˆ’(1Ɨ3) ] = 1 [15āˆ’(3 Ɨ4)]+2[āˆ’10āˆ’(āˆ’4)]+3[(2 Ɨ3)āˆ’3] = 1 [15āˆ’12]+2[āˆ’10+4]+3[6āˆ’3] = 1 [3]+2[āˆ’6]+3[3] = 3 ā€“ 12 + 9 = 0 Since [š‘Ž āƒ—" " š‘ āƒ—" " š‘ āƒ— ] = 0 Vectors š’‚ āƒ—, š’ƒ āƒ—, š’„ āƒ— are coplanar

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