Determine the vector product of V 1 → = 2 i + 3 j - k a n d V 1 → = i + 2 j - 3 k

Given, V 1 → = 2 i + 3 j - k V 2 → = i + 2 j - 3 k The cross-product of two vectors in the matrix/determinant form is given by, V 1 → × V 2 → = i j k v 1 x v 1 y v 1 z v 2 x v 2 y v 2 z V 1 → × V 2 → = i j k 2 3 - 1 1 2 - 3 V 1 → × V 2 → = i - 3 × 3 + 2 - j - 3 × 2 + 1 + k 2 × 2 - 3 × 1 V 1 → × V 2 → = - 7 i + 5 j + k Hence, the cross-product of the two given vectors is - 7 i + 5 j + k .

Determine the vector product of V 1 → = 2 i + 3 j - k a n d V 1 → = i + 2 j - 3 k

Given, V 1 → = 2 i + 3 j - k V 2 → = i + 2 j - 3 k The cross-product of two vectors in the matrix/determinant form is given by, V 1 → × V 2 → = i j k v 1 x v 1 y v 1 z v 2 x v 2 y v 2 z V 1 → × V 2 → = i j k 2 3 - 1 1 2 - 3 V 1 → × V 2 → = i - 3 × 3 + 2 - j - 3 × 2 + 1 + k 2 × 2 - 3 × 1 V 1 → × V 2 → = - 7 i + 5 j + k Hence, the cross-product of the two given vectors is - 7 i + 5 j + k .

Given V → 1 = 5 i + 2 j a n d V → 2 = a i - 6 j are perpendicular to each other determine the value of a.

Given vectors are V → 1 = 5 i + 2 j a n d V → 2 = a i - 6 j , If two vectors are perpendicular to each other, their Dot product is Zero V → 1 . V → 2 = 5 i + 2 j . a i - 6 j = 0 = 5 a - 12 = 0 a = 12 5

Obtain derivative of the following function i i i x sin x

Given function is f x = x sin x f ' x = d d x x sin x = 1 sin x d d x x + x d d x sin x - 1 = 1 sin x - x sin x - 2 cos x = 1 sin x - x cos x sin x 2 = sin x - x cos x sin x 2