Question

Let b = 4i + 3j and c be two vectors perpendicular to each other in the xy-plane. All vectors in the same plane having projections 1 and 2 along b and c respectively are given by​

Answer 1

Answer:

a and b are two vectors perpendicular to each other in x y plane.

so, a.b = 0

let b = xi + y j

so, (4 i+ 3 j).(xi + y j) = 0

or, 4 x + 3 y = 0.(1)

x = 3 y = -4

then, b = k(3 i - 4 j) , where k is constant.

Let α = (p i + q j) is required vector.

now, projection of α along a = (α.a)/|a| = 1

or, 1 = (pi + q j).(4 i + 3 j)/5

or, 5 = 4 p + 3 q (1)

again, projection of α on b = (α.b)/|b| = 2

or, 2 = (pi + q j)k(3 i - 4 j)/5 k

or, 10 = 3 p - 4 q

Answer 2

Talking about two perpendicular vectors,

The dot product of both is zero. Always.

Formula : a•b = ab cosα

The given vector is 4i-3j.

By the above formula we get,

(4i-3j).(ai+bj)=0

4a-3b=0

4a=3b

a/b=3/4

Therefore the vector perpendicular to given vector is 3i+4j.

Explanation:

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