हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा ११

Choose the correct alternative:If the projection of ijk5i^- j^-3k^ on the vector ijki^+3j^+λk^ is same as the projection of ijki^+3j^+λk^ on ijk5i^- j^-3k^, then λ is equal to - Mathematics

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • ± 4

  • ± 3

  • ± 5

  • ± 1

MCQ

उत्तर

± 5

shaalaa.com
Product of Vectors
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Vector Algebra - Exercise 8.5 [पृष्ठ ८२]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 8 Vector Algebra
Exercise 8.5 | Q 21 | पृष्ठ ८२

संबंधित प्रश्न

Show that the points (2, –1, 3), (4, 3, 1) and (3, 1, 2) are collinear


If `vec"a", vec"b"` are unit vectors and q is the angle between them, show that 

`cos  theta/2 = 1/2|vec"a" + vec"b"|`


If `vec"a", vec"b"` are unit vectors and q is the angle between them, show that 

`tan  theta/2 = |vec"a" - vec"b"|/|vec"a" + vec"b"|`


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


Find the angle between the vectors

`2hat"i" + 3hat"j" - 6hat"k"` and `6hat"i" - 3hat"j" + 2hat"k"`


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


Let `vec"a", vec"b", vec"c"` be three vectors such that `|vec"a"| = 3, |vec"b"| = 4, |vec"c"| = 5` and each one of them being perpendicular to the sum of the other two, find `|vec"a" + vec"b" + vec"c"|`


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 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)


Let `vec"a", vec"b", vec"c"` be unit vectors such that `vec"a" * vec"b" = vec"a"*vec"c"` = 0 and the angle between `vec"b"` and `vec"c"` is `pi/3`. Prove that `vec"a" = +-  2/sqrt(3) (vec"b" xx vec"c")`


Choose the correct alternative:
A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to


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


Choose the correct alternative:
If `vec"a"` and `vec"b"` having same magnitude and angle between them is 60° and their scalar product `1/2` is then `|vec"a"|` is


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:
Vectors `vec"a"` and `vec"b"` are inclined at an angle θ = 120°. If `vec"a"| = 1, |vec"b"| = 2`, then `[(vec"a" + 3vec"b") xx (3vec"a" - vec"b")]^2` 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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×