Advertisements
Advertisements
प्रश्न
If vectors `overset->a = 2hati + 2hatj + 3hatk, overset->b = -hati + 2hatj + hatk and overset->c = 3hati + hatj` are such that `overset->b + lambda overset->c` is perpendicular to `overset->a`, then find the value of λ.
योग
उत्तर
`overset->a = 2hati + 2hatj + 3hatk`
`overset->b = -hati + 2hatj + hatk`
`overset->c = 3hati + hatj`
`overset->b + lambda overset->c = (-hati + 2hatj + hatk) + lambda(3hati + hatj) = (-1 + 3lambda)hati + (2 + lambda)hatj + hatk`
`(overset->b + lambda overset->c) ⊥ overset->a`
`(overset->b + lambda overset->c)*overset->a = 0`
`=> [(-1 + 3lambda)hati + (2 + lambda)hatj + hatk] * (2hati + 2hatj + 3hatk) = 0`
`=> -2 + 6lambda + 4 + 2lambda + 3 = 0`
⇒ 8λ + 5 = 0
`lambda = -5/8`
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
