Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
If (1, 2, 4) and (2, – 3λ – 3) are the initial and terminal points of the vector `hat"i" + 5hat"j" - 7hat"k"` then the value of λ is equal to
विकल्प
`7/3`
`- 7/3`
` - 5/3`
`5/3`
उत्तर
`- 7/3`
APPEARS IN
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
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"|`
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"`
Find the projection of the vector `hat"i" + 3hat"j" + 7hat"k"` on the vector `2hat"i" + 6hat"j" + 3hat"k"`
Find the magnitude of `vec"a" xx vec"b"` if `vec"a" = 2hat"i" + hat"j" + 3hat"k"` and `vec"b" = 3hat"i" + 5hat"j" - 2hat"k"`
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" + vec"b"| = 60, |vec"a" - vec"b"| = 40` and `|vec"b"| = 46`, 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" + 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
