Home › JEE Advanced › Mathematics › Vector Algebra › Vector r̄ is collinear with ā = î - 2ĵ + 2k̂ and…
Vector r̄ is collinear with ā = î - 2ĵ + 2k̂ and |r̄| = 12. Find r̄:
A4î - 8ĵ + 8k̂
Bî - 2ĵ + 2k̂
C12î - 24ĵ + 24k̂
D4î + 8ĵ + 8k̂
Answer & Solution
Correct answer: A. 4î - 8ĵ + 8k̂
Unit vector in direction of ā: â = ā/|ā| = (î - 2ĵ + 2k̂)/√(1+4+4) = (1/3)(î - 2ĵ + 2k̂). Vector of magnitude 12: r̄ = 12â = 4î - 8ĵ + 8k̂. Check: |r̄| = √(16+64+64) = √144 = 12 ✓.
Related questions
The result a cross b is a:The area of a triangle from its three vertices can be found using:The area of a parallelogram with sides a and b uses the magnitude of their:For mutually perpendicular unit vectors, i cross j equals:The cross product of two nonzero vectors is zero when they are:The angle between two vectors can be found in terms of their:The vector product is an operation that is:The scalar product is an operation that is: