16:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 17:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 15:T501,{"@context":"https://schema.org","@type":"Quiz","name":"Kcet 2026 Vector Algebra PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/kcet/questions/2026/mathematics/vector-algebra/jt-mr7eh8z6","educationalLevel":"Entrance exam preparation","about":"Kcet / Mathematics / Vector Algebra","hasPart":{"@type":"Question","name":"Kcet 2026 Vector Algebra PYQ with Solution","text":"If \\vec{a} = 2\\hat{i} + 2\\hat{j} - \\hat{k}, \\vec{b} = \\alpha\\hat{i} + \\beta\\hat{j} + 2\\hat{k} and |\\vec{a} + \\vec{b}| = |\\vec{a} - \\vec{b}|, then \\alpha + \\beta is equal to","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"D"},"comment":{"@type":"Comment","text":"Given \\vec{a}=2\\hat{i}+2\\hat{j}-\\hat{k} and \\vec{b}=\\alpha \\hat{i}+\\beta \\hat{j}+2\\hat{k} Also, |\\vec{a}+\\vec{b}|=|\\vec{a}-\\vec{b}| Square both sides: |\\vec{a}+\\vec{b}|^2=|\\vec{a}-\\vec{b}|^2 Using the identity, |\\vec{x}|^2=\\vec{x}\\cdot \\vec{x} we get (\\vec{a}+\\vec{b})\\cdot(\\vec{a}+\\vec{b})=(\\vec{a}-\\vec{b})\\cdot(\\vec{a}-\\vec{b}) Expanding both sides: |\\vec{a}|^2+2\\vec{a}\\cdot\\vec{b}+|\\vec{b}|^2 = |\\vec{a}|^2-2\\vec{a}\\cdot\\vec{b}+|\\vec{b}|^2 Cancel common terms: 2\\vec{a}\\cdot\\vec{b}=-2\\vec{a}\\cd..."}}}18:T446,

Given

$$ \vec{a}=2\hat{i}+2\hat{j}-\hat{k} $$

and

$$ \vec{b}=\alpha \hat{i}+\beta \hat{j}+2\hat{k} $$

Also,

$$ |\vec{a}+\vec{b}|=|\vec{a}-\vec{b}| $$

Square both sides:

$$ |\vec{a}+\vec{b}|^2=|\vec{a}-\vec{b

Vector Algebra

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