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Choose the correct alternative:If ijkλi^+2λj^+2λk^ is a unit vector, then the value of λ is - Mathematics

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प्रश्न

Choose the correct alternative:
If `lambdahat"i" + 2lambdahat"j" + 2lambdahat"k"` is a unit vector, then the value of `lambda` is

पर्याय

  • `1/3`

  • `1/4`

  • `1/9`

  • `1/2`

MCQ

उत्तर

`1/3`

shaalaa.com
Product of Vectors
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Vector Algebra - Exercise 8.5 [पृष्ठ ८१]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 8 Vector Algebra
Exercise 8.5 | Q 13 | पृष्ठ ८१

संबंधित प्रश्‍न

Show that the vectors `- 2hat"i" - hat"j" - hat"k", - 3hat"i" - 4hat"j" - 4hat"k", hat"i" - 3hat"j" - 5hat"k"` form a right angled triangle


Find `vec"a"*vec"b"` when `vec"a" = 2hat"i" + 2hat"j" - hat"k"` and `vec"b" = 6hat"i" - 3hat"j" + 2hat"k"`


Find the value λ for which the vectors `vec"a"` and  `vec"b"` are perpendicular, where `vec"a" = 2hat"i" + lambdahat"j" + hat"k"` and `vec"b" = hat"i" - 2hat"j" + 3hat"k"`


Find the value λ for which the vectors `vec"a"` and `vec"b"` are perpendicular, where `vec"a" = 2hat"i" + 4hat"j" - hat"k"` and `vec"b" = 3hat"i" - 2hat"j" + lambdahat"k"`


If `vec"a"` and `vec"b"` are two vectors such that `|vec"a"| = 10, |vec"b"| = 15` and `vec"a"*vec"b" = 75sqrt(2)`, find the angle between `vec"a"` and `vec"b"`


If `vec"a", vec"b", vec"c"` are three vectors such that `vec"a" + 2vec"b" + vec"c"` = 0 and `|vec"a"| = 3, |vec"b"| = 4, |vec"c"| = 7`, find the angle between `vec"a"` and `vec"b"`


Show that the vectors `vec"a" = 2hat"i" + 3hat"j" + 3hat"j" + 6hat"k", vec"b" = 6hat"i" + 2hat"j" - 3hat"k"` and `vec"c" = 3hat"i" - 6hat"j" + 6hat"k"` are mutually orthogonal


Show that the vectors `-hat"i" - 2hat"j" - 6hat"k", 2hat"i" - hat"j" + hat"k"` and find `-hat"i" + 3hat"j" + 5hat"k"` form a right angled triangle


Show that `vec"a" xx (vec"b" + vec"c") + vec"b" xx (vec"c" + vec"a") + vec"c" xx (vec"a" + vec"b") = vec0`


Find the unit vectors perpendicular to each of the vectors `vec"a" + vec"b"` and `vec"a" - vec"b"`, where `vec"a" = hat"i" + hat"j" + hat"k"` and `vec"b" = hat"i" + 2hat"j" + 3hat"k"`


Find the area of the parallelogram whose two adjacent sides are determined by the vectors  `hat"i" + 2hat"j" + 3hat"k"` and `3hat"i" - 2hat"j" + hat"k"`


Find the area of the triangle whose vertices are A(3, – 1, 2), B(1, – 1, – 3) and C(4, – 3, 1)


Choose the correct alternative:
The value of θ ∈ `(0, pi/2)` for which the vectors `"a" = (sin theta)hat"i" = (cos theta)hat"j"` and `vec"b" = hat"i" - sqrt(3)hat"j" + 2hat"k"` are perpendicular, equaal to


Choose the correct alternative:
If `|vec"a"| = 13, |vec"b"| = 5` and `vec"a" * vec"b"` = 60° then `|vec"a" xx vec"b"|` is  


Choose the correct alternative:
If `vec"a"` and `vec"b"` are two vectors of magnitude 2 and inclined at an angle 60°, then the angle between `vec"a"` and `vec"a" + vec"b"` is


Choose the correct alternative:
If the projection of `5hat"i" -  hat"j" - 3hat"k"` on the vector `hat"i" + 3hat"j" + lambdahat"k"` is same as the projection of `hat"i" + 3hat"j" + lambdahat"k"` on `5hat"i" -  hat"j" - 3hat"k"`, then λ is equal to


Choose the correct alternative:
If `vec"a" = hat"i" + hat"j" + hat"k", vec"b" = 2hat"i" + xhat"j" + hat"k", vec"c" = hat"i" - hat"j" + 4hat"k"` and `vec"a" * (vec"b" xx vec"c")` = 70, then x is equal to


Choose the correct alternative:
If `vec"a" = hat"i" + 2hat"j" + 2hat"k", |vec"b"|` = 5 and the angle between `vec"a"` and `vec"b"` is `pi/6`, then the area of the triangle formed by these two vectors as two sides, is


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