हिंदी

Let ̅𝑎 =̂𝑖 +2⁢̂𝑗 +̂𝑘,̅𝑏 =̂𝑖 −̂𝑗 +̂𝑘⁢and⁢̅𝑐 =̂𝑖 +̂𝑗 −̂𝑘. A vector in the plane of ̅𝑎⁢and⁢̅𝑏 whose projection on ̅𝑐 is 1/√3, is

Let `bara = hati + 2hatj + hatk, barb = hati - hatj + hatk and barc = hati + hatj - hatk`.

A vector in the plane of `bara and barb` whose projection on `barc` is `1/sqrt3`, is

MCQ

`bb(4hati - hatj + 4hatk)`

Explanation:

A vector in the plane of `bara and hatb` is

`baru = bara + lambdabarb = (1 + lambda)hati + (2 - lambda)hatj + (1 + lambda)hatk`

Projection of `baru` on `barc = 1/sqrt3`

= `(baru.barc)/(|barc|) = 1/sqrt3`

= `baru.barc = 1 = |1 + lambda + 2 - lambda - 1 - lambda| = 1`

= |2 − λ| = 1 = λ = 1 or 3

= `batu = 2hati + hatj + 2hatk` or `4hati - hatj + 4hatk`

shaalaa.com

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Notifications