Question 11 - CBSE Class 12 Sample Paper for 2018 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at July 29, 2026 by

Find the Projection (vector) of 2i − j + k on i − 2j + k

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

You can download the question paper here  https://www.teachoo.com/cbse/sample-papers/

Find Projection (vector) of 2i - j + k on i - 2j + k - Teachoo

Question 11 - CBSE Class 12 Sample Paper for 2018 Boards - Part 2
Question 11 - CBSE Class 12 Sample Paper for 2018 Boards - Part 3

Remove Ads

Transcript

Question 11 Find the Projection (vector) of 2š‘– Ģ‚ āˆ’ š‘— Ģ‚ + š‘˜ Ģ‚ on š‘– Ģ‚ āˆ’ 2š‘— Ģ‚ + š‘˜ Ģ‚ Let a = 2š‘– Ģ‚ āˆ’ š‘— Ģ‚ + š‘˜ Ģ‚ and b = š‘– Ģ‚ āˆ’ 2š‘— Ģ‚ + š‘˜ Ģ‚ We need to find Projection (vector) of š‘Ž āƒ— on š‘ āƒ— Theory We know that Projection of š‘Ž āƒ— on š‘ āƒ— = 1/("|" š‘ āƒ—"|" ) (š‘Ž āƒ—. š‘ āƒ—) But here, we are asked projection (vector) So, we multiply projection by š‘ āƒ—/|š‘ āƒ— | Projection (vector) of š‘Ž āƒ— on š‘ āƒ— = 1/|š‘ āƒ— | (š‘Ž āƒ—. š‘ āƒ—) Ɨ š‘ āƒ—/|š‘ āƒ— | = ((š‘Ž āƒ— . š‘ āƒ— ))/|š‘ āƒ— |^2 Ɨ š‘ āƒ— (š’‚ āƒ—. š’ƒ āƒ—) = (2 Ɨ 1) + (ā€“1 Ɨ ā€“2) + (1 Ɨ 1) = 2 + 2 + 1 = 5 Magnitude of š‘ āƒ— = āˆš(12+(āˆ’2)2+12) |š‘ āƒ— | = āˆš(1+4+1) = āˆš6 Projection (vector) of š’‚ āƒ— on š’ƒ āƒ— = ((š‘Ž āƒ— . š‘ āƒ— ))/|š‘ āƒ— |^2 Ɨ š‘ āƒ— = 5/(āˆš6)^2 Ɨ ( š‘– Ģ‚ āˆ’ 2š‘— Ģ‚ + š‘˜ Ģ‚) = šŸ“/šŸ” ( š’Š Ģ‚ āˆ’ 2š’‹ Ģ‚ + š’Œ Ģ‚)

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.