The scalar projection of the vector 3i ฬ-j ฬ-2k ฬ ๐๐ ๐กโ๐ ๐ฃ๐๐๐ก๐๐ i ฬ+2j ฬ-3k ฬ is
(a) 7/โ14 ย
(b) 7/14 ย
(c) 6/13 ย
(d) 7/2
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CBSE Class 12 Sample Paper for 2023 Boards
Last updated at March 22, 2023 by Teachoo
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Question 8 The scalar projection of the vector 3๐ ฬโ๐ ฬโ2๐ ฬ ๐๐ ๐กโ๐ ๐ฃ๐๐๐ก๐๐ ๐ ฬ+2๐ ฬโ3๐ ฬ is (a) 7/โ14 (b) 7/14 (c) 6/13 (d) 7/2 Let a = 3๐ ฬ โ ๐ ฬ โ 2๐ ฬ and b = ๐ ฬ + 2๐ ฬ โ 3๐ ฬ We need to find Projection of ๐ โ on ๐ โ We know that Projection of ๐ โ on ๐ โ = ๐/("|" ๐ โ"|" ) (๐ โ. ๐ โ) Now, (๐ โ. ๐ โ) = (3๐ ฬ โ ๐ ฬ โ 2๐ ฬ ) . (๐ ฬ + 2๐ ฬ โ 3๐ ฬ) = (3 ร 1) + (โ1 ร 2) + (โ2 ร โ3) = 7 Magnitude of ๐ โ = โ(12+22+(โ3) 2) |๐ โ | = โ(1+4+9) = โ๐๐ Thus, Projection of ๐ โ on ๐ โ = 1/("|" ๐ โ"|" ) (๐ โ. ๐ โ) = ๐/โ๐๐ So, the correct answer is (a)