Advertisements
Advertisements
प्रश्न
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"`
उत्तर
When `vec"a"` and `vec"b"` are ⊥r then `vec"a"*vec"b"` = 0
`vec"a"` ⊥r `vec"b"` ⇒ `vec"a" * vec"b"` = 0
(2)(1) + (λ)(– 2) + (1)(3) = 0
⇒ λ = `5/2`
APPEARS IN
संबंधित प्रश्न
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" = hat"i" - 2hat"j" + hat"k"` and `vec"b" = 3hat"i" - 4hat"j" - 2hat"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"`
Find the angle between the vectors
`2hat"i" + 3hat"j" - 6hat"k"` and `6hat"i" - 3hat"j" + 2hat"k"`
Find the angle between the vectors
`hat"i" - hat"j"` and `hat"j" - hat"k"`
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"`
Find the projection of the vector `hat"i" + 3hat"j" + 7hat"k"` on the vector `2hat"i" + 6hat"j" + 3hat"k"`
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 triangle whose vertices are A(3, – 1, 2), B(1, – 1, – 3) and C(4, – 3, 1)
If `vec"a", vec"b", vec"c"` are position vectors of the vertices A, B, C of a triangle ABC, show that the area of the triangle ABC is `1/2 |vec"a" xx vec"b" + vec"b" xx vec"c" + vec"c" xx vec"a"|`. Also deduce the condition for collinearity of the points A, B, and C
Choose the correct alternative:
The vectors `vec"a" - vec"b", vec"b" - vec"c", vec"c" - vec"a"` are
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"` 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 `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
